Avogadro’s Law Avogadro’s Law is one of the gas laws. At the beginning of the 19th century, an Italian scientist Lorenzo Romano Amedeo Carlo Avogadro studied the relationship between the volume and the amount of substance of gas present. The results of certain experiments with gases led him to formulate a well-known Avogadro’s Law. Avogadros law synonyms, Avogadros law pronunciation, Avogadros law translation, English dictionary definition of Avogadros law. The principle that equal volumes of all gases at the same temperature and pressure contain the same number of molecules. Avogadro’s law is a gas law and is also referred to as Avogadro’s hypothesis or Avogadro’s principle. It states that the total number of molecules or atoms of a gas is directly proportional to the volume that the gas occupies at a constant temperature and pressure. Avogadro's law investigates the relationship between the amount of gas (n) and volume (v). It's a direct relationship, meaning the volume of a gas is directly propotional to the number of moles the gas sample present. The constants in this relationship would be the temperature (t) and pressure (p) The equation for this law is: n1/v1 = n2/v2.
Avogadro's Law:
Ten Examples
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Discovered by Amedo Avogadro, of Avogadro's Hypothesis fame. The ChemTeam is not sure when, but probably sometime in the early 1800s.
Gives the relationship between volume and amount when pressure and temperature are held constant. Remember amount is measured in moles. Also, since volume is one of the variables, that means the container holding the gas is flexible in some way and can expand or contract.
If the amount of gas in a container is increased, the volume increases.
If the amount of gas in a container is decreased, the volume decreases.
Why?
Suppose the amount is increased. This means there are more gas molecules and this will increase the number of impacts on the container walls. This means the gas pressure inside the container will increase (for an instant), becoming greater than the pressure on the outside of the walls. This causes the walls to move outward. Since there is more wall space the impacts will lessen and the pressure will return to its original value.
The mathematical form of Avogadro's Law is:
| V | |
| ––– | = k |
| n |
This means that the volume-amount fraction will always generate a constant if the pressure and temperature remain constant.
Let V1 and n1 be a volume-amount pair of data at the start of an experiment. If the amount is changed to a new value called n2, then the volume will change to V2.
We know this:
| V1 | |
| ––– | = k |
| n1 |
And we know this:
| V2 | |
| ––– | = k |
| n2 |
Since k = k, we can conclude:
| V1 | V2 | |
| ––– | = | ––– |
| n1 | n2 |
This equation will be very helpful in solving Avogadro's Law problems. You will also see it rendered thusly:
V1 / n1 = V2 / n2
Sometimes, you will see Avogadro's Law in cross-multiplied form:
V1n2 = V2n1
Avogadro's Law is a direct mathematical relationship. If one gas variable (V or n) changes in value (either up or down), the other variable will also change in the same direction. The constant K will remain the same value.
Example #1: 5.00 L of a gas is known to contain 0.965 mol. If the amount of gas is increased to 1.80 mol, what new volume will result (at an unchanged temperature and pressure)?
Solution:
I'll use V1n2 = V2
n1(5.00 L) (1.80 mol) = (x) (0.965 mol)
x = 9.33 L (to three sig figs)
Example #2: A cylinder with a movable piston contains 2.00 g of helium, He, at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many grams of helium were added to the cylinder if the volume was changed from 2.00 L to 2.70 L? (The temperature was held constant.)
Solution:
1) Convert grams of He to moles:
2.00 g / 4.00 g/mol = 0.500 mol
2) Use Avogadro's Law:
V1 / n1 = V2 / n22.00 L / 0.500 mol = 2.70 L / x
x = 0.675 mol
3) Compute grams of He added:
0.675 mol − 0.500 mol = 0.175 mol(0.175 mol) (4.00 g/mol) = 0.7 grams of He added
Example #3: A balloon contains a certain mass of neon gas. The temperature is kept constant, and the same mass of argon gas is added to the balloon. What happens?
(a) The balloon doubles in volume.
(b) The volume of the balloon expands by more than two times.
(c) The volume of the balloon expands by less than two times.
(d) The balloon stays the same size but the pressure increases.
(e) None of the above.
Solution:
We can perform a calculation using Avogadro's Law:V1 / n1 = V2 / n2
Let's assign V1 to be 1 L and V2 will be our unknown.
Let us assign 1 mole for the amount of neon gas and assign it to be n1.
The mass of argon now added is exactly equal to the neon, but argon has a higher gram-atomic weight (molar mass) than neon. Therefore less than 1 mole of Ar will be added. Let us use 1.5 mol for the total moles in the balloon (which will be n2) after the Ar is added. (I picked 1.5 because neon weighs about 20 g/mol and argon weighs about 40 g/mol.)
1 / 1 = x / 1.5
x = 1.5
answer choice (c).
Example #4: A flexible container at an initial volume of 5.120 L contains 8.500 mol of gas. More gas is then added to the container until it reaches a final volume of 18.10 L. Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container.
Solution:
V1 / n1 = V2 / n2| 5.120 L | 18.10 L | |
| –––––––– | = | –––––– |
| 8.500 mol | x |
x = 30.05 mol <--- total moles, not the moles added
30.05 − 8.500 = 21.55 mol (to four sig figs)
Notice the specification in the problem to determine moles of gas added. The Avogadro Law calculation gives you the total moles required for that volume, NOT the moles of gas added. That's why the subtraction is there.
Example #5: If 0.00810 mol neon gas at a particular temperature and pressure occupies a volume of 214 mL, what volume would 0.00684 mol neon gas occupy under the same conditions?
Solution:
1) Notice that the same conditions are the temperature and pressure. Holding those two constant means the volume and the number of moles will vary. The gas law that describes the volume-mole relationship is Avogadro's Law:
| V1 | V2 | |
| ––– | = | –––– |
| n1 | n2 |
2) Substituting values gives:
| 214 mL | V2 | |
| ––––––––– | = | –––––––––– |
| 0.00810 mol | 0.00684 mol |
3) Cross-multiply and divide for the answer:
V2 = 181 mL (to three sig figs)When I did the actual calculation for this answer, I used 684 and 810 when entering values into the calculator.
4) You may find this answer interesting:
Dividing PV1 = n1RT by PV2 = n2RT, we getV1/V2 = n1/n2
V2 = V1n2/n1
V2 = [(214 mL) (0.00684 mol)] / 0.00810 mol
V2 = 181 mL
In case you don't know, PV = nRT is called the Ideal Gas Law. You'll see it a bit later in your Gas Laws unit, if you haven't already.
Example #6: A flexible container at an initial volume of 6.13 L contains 7.51 mol of gas. More gas is then added to the container until it reaches a final volume of 13.5 L. Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container.
Solution:
1) Let's start by rearranging the Ideal Gas Law (which you'll see a bit later or you can go review it right now):
PV = nRTV/n = RT / P
R is, of course, a constant.
2) T and P are constant, as stipulated in the problem. Therefore, we can write this:
k = RT / Pwhere k is some constant.
3) Therefore, this is true:
V/n = k
4) Given V and n at two different sets of conditions, we have:
V1 / n1 = k
V2 / n2 = k
5) Since k = k, we have this relation:
V1 / n1 = V2 / n2
6) Insert data and solve:
6.13 / 7.51 = 13.5 / n(6.13) (n) = (13.5) (7.51)
n = [(13.5) (7.51)] / 6.13
n = 16.54 mol (this is not the final answer)
7) Final step:
16.54 − 7.51 = 9.03 mol (this is the number of moles of gas that were added)
Example #7: A container with a volume of 25.47 L holds 1.050 mol of oxygen gas (O2) whose molar mass is 31.9988 g/mol. What is the volume if 7.210 g of oxygen gas is removed from the container, assuming the pressure and temperature remain constant?
Solution #1:
1) Initial mass of O2:
(1.050 mol) (31.9988 g/mol) = 33.59874 g
2) Final mass of O2:
33.59874 − 7.210 = 26.38874 g
3) Final moles of O2:
26.38874 g / 31.9988 g/mol = 0.824679 mol
4) Use Avogadro's Law:
V1 / n1 = V2 / n225.47 L / 1.050 mol = V2 / 0.824679 mol
V2 = 20.00 L
Solution #2:
1) Let's convert the mass of O2 removed to moles:
7.210 g / 31.9988 g/mol = 0.225321 mol
2) Subtract moles of O2 that got removed:
1.050 mol − 0.225321 mol = 0.824679 mol
3) Use Avogadro's Law as above.
Solution #3:
1) This solution depends on seeing that the mass ratio is the same as the mole ratio. Allow me to explain by using Avogadro's Law:
| V1 | V2 | |
| –––– | = | –––– |
| n1 | n2 |
2) Replace moles with mass divided by molar mass:
| V1 | V2 | |
| –––––––––– | = | –––––––––– |
| mass1 / MM | mass2 / MM |
3) Since the molar mass is of the same substance (oxygen in this case), they cancel out leaving us with this:
| V1 | V2 | |
| –––– | = | –––– |
| mass1 | mass2 |
4) Solve using the appropriate values
| 25.47 L | V2 | |
| –––––––– | = | –––––––– |
| 33.59874 g | 26.38874 g |
V2 = 20.00 L
Example #8: What volume (in L) will 5.5 g of oxygen gas occupy if 2.2 g of the oxygen gas occupies 3.0 L? (Under constant pressure and temperature.)
Avogadro's Law Experiments
Solution:
1) State the ideal gas law:
| P1V1 | P2V2 | |
| ––––– | = | ––––– |
| n1T1 | n2T2 |
Note that it is the full version which includes the moles of gas. Usually a shortened version with the moles not present is used. Since grams are involved (which leads to moles), we choose to use the full version.
2) The problem states that P and T are constant:
| V1 | V2 | |
| ––– | = | ––– |
| n1 | n2 |
3) Cross-multiply and rearrange to isolate V2:
V2n1Avogadro's Law Meaning
= V1
n2V2 = (V1) (n2 / n1)
4) moles = mass / molecular weight:
n = mass / mwV2 = (V1) [(mass2 / mw) / (mass1 / mw)]
5) mw is a constant (since they are both the molecular weight of oxygen), which means it can be canceled out:
V2 = (V1) (mass2 / mass1)
6) Solve:
V2 = (3.0 L) (5.5 g / 2.2 g)V2 = 7.5 L
Example #9: At a certain temperature and pressure, one mole of a diatomic H2 gas occupies a volume of 20 L. What would be the volume of one mole of H atoms under those same conditions?
Solution:
One mole of H2 molecules has 6.022 x 1023 H2 molecules.One mole of H atoms has 6.022 x 1023 H atoms.
The number of independent 'particles' in each sample is the same.
Therefore, the volumes occupied by the two samples are the same. The volume of the H atoms sample is 20 L.
By the way, I agree that one mole of H2 has twice as many atoms as one mole of H atoms. However, the atoms in H2 are bound up into one mole of molecules, which means that one molecule of H2 (with two atoms) counts as one independent 'particle' when considering gas behavior.
Example #10: A flexible container at an initial volume of 6.13 L contains 8.51 mol of gas. More gas is then added to the container until it reaches a final volume of 15.5 L. Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container.
Solution:
1) State Avogadro's Law in problem-solving form:
| V1 | V2 | |
| ––– | = | –––– |
| n1 | n2 |
2) Substitute values into equation and solve:
| 6.13 L | 15.5 L | |
| ––––––– | = | –––––– |
| 8.51 mol | x |
x = 21.5 mol
3) Determine moles of gas added:
21.5 mol − 8.51 mol = 13.0 mol (when properly rounded off)
Bonus Example: A cylinder with a movable piston contains 2.00 g of helium, He, at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many grams of helium were added to the cylinder if the volume was changed from 2.00 L to 2.50 L? (The temperature was held constant.)
Solution:
1) The two variables are the volume and the amount of gas (temp and press are constant). The gas law that relates these two variables is Avogadro's Law:
| V1 | V2 | |
| ––– | = | –––– |
| n1 | n2 |
2) We convert the grams to moles:
2.00 g / 4.00 g/mol = 0.500 mol
3) Now, we use Avogadro's Law:
| 2.00 L | 2.50 L | |
| –––––––– | = | –––––– |
| 0.500 mol | x |
x = [(0.500 mol) (2.50 L)] / 2.00 L
Avogadro's Law Example
x = 0.625 mol <--- this is the ending amount of moles, not the moles of gas added
4) This is the total moles to create the 2.50 L. We need to convert back to grams:
(4.00 g/mol) (0.125 mol) = 0.500 g <--- this is the amount added.Notice that I subtracted 0.500 mol from 0.625 mol and used 0.125 mol in the calculation. This is because I want the amount added, not the final ending amount.
Avogadro's Law Meaning
| Boyle's Law | Combined Gas Law |
| Charles' Law | Ideal Gas Law |
| Gay-Lussac's Law | Dalton's Law |
| Diver's Law | Graham's Law |
| No Name Law | Return to KMT & Gas Laws Menu |
Law
A body of rules of conduct of binding legal force and effect, prescribed, recognized, and enforced by controlling authority.
In U.S. law, the word law refers to any rule that if broken subjects a party to criminal punishment or civil liability. Laws in the United States are made by federal, state, and local legislatures, judges, the president, state governors, and administrative agencies.
Law in the United States is a mosaic of statutes, treaties, case law, Administrative Agency regulations, executive orders, and local laws. U.S. law can be bewildering because the laws of the various jurisdictions—federal, state, and local—are sometimes in conflict. Moreover, U.S. law is not static. New laws are regularly introduced, old laws are repealed, and existing laws are modified, so the precise definition of a particular law may be different in the future from what it is today.
The U.S. Constitution
The highest law in the United States is the U.S. Constitution. No state or federal law may contradict any provision in the Constitution. In a sense the federal Constitution is a collection of inviolable statutes. It can be altered only by amendment. Amendments pass after they are approved by two-thirds of both houses of Congress or after petition by two-thirds of the state legislatures. Amendments are then ratified by three-fourths of the state legislatures or by conventions in three-fourths of the states. Upon ratification, the amendment becomes part of the Constitution.
Beneath the federal Constitution lies a vast body of other laws, including federal statutes, treaties, court decisions, agency regulations, and executive orders, and state constitutions, statutes, court decisions, agency regulations, and executive orders.
Statutes and Treaties
After the federal Constitution, the highest laws are written laws, or statutes, passed by elected federal lawmakers. States have their own constitution and statutes.
Federal laws generally involve matters that concern the entire country. State laws generally do not reach beyond the borders of the state. Under Article VI, Section 2, of the U.S. Constitution, federal laws have supremacy over state and local laws. This means that when a state or local law conflicts with a federal law, the federal law prevails.
Federal statutes are passed by Congress and signed into law by the president. State statutes are passed by state legislatures and approved by the governor. If a president or governor vetoes, or rejects, a proposed law, the legislature may override the Veto if at least two-thirds of the members of each house of the legislature vote for the law.
Statutes are contained in statutory codes at the federal and state levels. These statutory codes are available in many public libraries, in law libraries, and in some government buildings, such as city halls and courthouses. They are also available on the World Wide Web. For example, the statutory codes that are in effect in the state of Michigan can be accessed at <http://www.michigan.gov/orr>. A researcher may access the United States Code, which is the compilation of all federal laws, at <http://uscode.house.gov>. The site is maintained by the Office of the Law Revision Counsel of the U.S. House of Representatives.
On the federal level, the president has the power to enter into treaties, with the advice and consent of Congress. Treaties are agreements with sovereign nations concerning a wide range of topics such as environmental protection and the manufacture of nuclear missiles. A treaty does not become law until it is approved by two-thirds of the U.S. Senate. Most treaties are concerned with the actions of government employees, but treaties also apply to private citizens.
Case Law
Statutes are the primary source of law, and the power to enact statutes is reserved to elected lawmakers. However, judicial decisions also have the force of law. Statutes do not cover every conceivable case, and even when a statute does control a case, the courts may need to interpret it. Judicial decisions are known collectively as case law. A judicial decision legally binds the parties in the case, and also may serve as a law in the same prospective sense as does a statute. In other words, a judicial decision determines the outcome of the particular case, and also may regulate future conduct of all persons within the jurisdiction of the court.
The opinions of courts, taken together, comprise the Common Law. When there is no statute specifically addressing a legal dispute, courts look to prior cases for guidance. The issues, reasoning, and holdings of prior cases guide courts in settling similar disputes. A prior opinion or collection of opinions on a particular legal issue is known as precedent, and courts generally follow precedent, if any, when deciding cases. Breaking with precedent may be justified when circumstances or attitudes have changed, but following precedent is the norm. This gives the common law a certain predictability and consistency. The common law often controls civil matters, such as contract disputes and personal injury cases (torts). Almost all criminal laws are statutory, so common law principles are rarely applied in criminal cases.
Sometimes courts hear challenges to statutes or regulations based on constitutional grounds. Courts can make law by striking down part or all of a particular piece of legislation. The Supreme Court has the power to make law binding throughout the country on federal constitutional issues. The highest court in each state has the same power to interpret the state constitution and to issue holdings that have the force of law.
Occasionally courts create new law by departing from existing precedent or by issuing a decision in a case involving novel issues, called a case of first impression. If legislators disagree with the decision, they may nullify the holding by passing a new statute. However, if the court believes that the new statute violates a constitutional provision, it may strike down all or part of the new law. If courts and lawmakers are at odds, the precise law on a certain topic can change over and over.
Common-Law Courts
Courts of law are a fundamental part of the U.S. judicial system. The U.S. Constitution and all state constitutions recognize a judicial branch of government that is charged with adjudicating disputes. Beginning in the 1990s, vigilante organizations challenged the judicial system by establishing their own so-called common-law courts. By 1996 these common-law courts existed in more than 30 states. Though they have no legitimate power, being created without either constitutional or statutory authority, and in fact sometimes contravene established law.
Traditionally, common-law courts administered the Common Law, that is, law based on prior decisions rather than statutes. These new common-law courts, however, are premised on a mixture of U.S. Constitutional Law, English common law, and the Bible, all filtered through an often racist and anti-Semitic world view that holds the U.S. legal system to be illegitimate. These common-law courts imitate the formalities of the U.S. justice system, issuing subpoenas, making criminal indictments, and hearing cases. Most of their cases involve Divorce decrees and foreclosure actions. Many of the persons on the courts or seeking their assistance are in dire financial circumstances. They wish to prevent the loss of their property by having a common-law court declare them free of the loans they have secured from banks.
Though common-law courts appeared to be merely a symbolic attempt by extremists to assert their political legitimacy, the actions of some of them led to prosecution for criminal conspiracy. Common-law courts have issued arrest warrants for judges and prosecutors in Montana and Idaho and have threatened sheriffs who refused to follow their instructions. In 1994 the Garfield County, Montana, prosecutor charged members of a common-law court with criminal syndicalism, for advocating violence against public officials. One court member was sentenced to ten years in prison, and others received shorter sentences.
When researching a legal issue, it is helpful to consult relevant case law. The researcher first finds the relevant annotated statutes, and then reads the cases that are listed under the statutes. Reading case law helps the researcher understand how the courts interpret statutes, and also how the courts analyze related issues that are not covered in the statutes. Volumes of case law can be found in some public libraries, in law libraries, in courthouses, and in state government buildings such as statehouses and state libraries. Case law research can also be conducted using the Internet. For example, Cornell University's online Legal Information Institute (<http://www.law.cornell.edu>) offers recent and historic U.S. Supreme Court decisions, as well as recent New York appeals decisions.
Agency Regulations and Executive Orders
Administrative agencies may also create laws. The federal and state constitutions implicitly give the legislatures the power to create administrative agencies. Administrative agencies are necessary because lawmakers often lack detailed knowledge about important issues, and they need experts to manage the regulation of complex subjects. On the federal level, for example, the Department of the Interior was created by Congress to manage the nation's natural resources. In creating the agency, Congress gave it power to promulgate regulations concerning the use and protection of natural resources.
Administrative agency regulations have the force of law if they have a binding effect on the rights and duties of persons. For example, Interior Department regulations that prohibit mining or logging in certain areas of the country are considered law, even though they are not formulated by an elected official or judge. Federal administrative agency rules are approved by Congress, so ultimately they are a product of the will of elected officials. Similarly, on the state and local levels, an administrative agency may promulgate rules that have the force of law, but only at the pleasure of the elected lawmakers that created the agency. If an agency seeks to change a regulation, it must, in most cases, inform the public of its intentions and provide the public with an opportunity to voice concerns at a public meeting.
Not all agency regulations have the force of law. Agency rules that merely interpret other rules, state policy, or govern organization, procedure, and practice need not be obeyed by parties outside the agency.
Some administrative agencies have Quasi-Judicial powers. That is, they have limited authority to hear disputes and make binding decisions on matters relevant to the agency. For example, the Health and Human Services Department (HHS) has a court with authority to hear cases concerning actions by the HHS, such as the denial of Social Security benefits. An administrative law judge (ALJ) presides over the court, and appeals from ALJ decisions can be taken to an HHS appeals council. If an administrative agency has quasi-judicial powers, decisions made by the ALJ and boards of appeals have the force of law.
The quickest way to uncover information about state agency regulations is to search the World Wide Web. Most state agencies maintain a comprehensive website. Each state's Secretary of State can also be accessed on the Web. Most agencies are named according to their area of concern. For example, a department of Gaming is concerned with gambling, and a department of fish, game, and wildlife is concerned with issues related to hunting and wildlife conservation.
Executive orders are issued to interpret, implement, or administer laws. On the federal level, executive orders are issued by the president or by another Executive Branch official under the president's direction. Executive orders range from commands for detailed changes in federal administrative agency procedures to commands for military action. To have the force of law, a federal Executive Order must be published in the Federal Register, the official government publication of executive orders and federal administrative agency regulations. On the state level, governors have similar authority to make laws concerning state administrative agencies and state military personnel.
Avogadro's Law Meaning Wikipedia
Local Laws
Counties, cities, and towns also have the authority to make laws. Local laws are issued by elected lawmakers and local administrative agencies. Local laws cannot conflict with state or federal laws. Decisions by local courts generally operate as law insofar as they apply to the participants in the case. To a lesser extent, local court decisions may have a prospective effect. That is, a local court decision can operate as precedent, but only in cases brought within the same jurisdiction. For example, a decision by a court in Green County may affect future court cases in Green County, but it has no bearing on the law in any other county. Local laws can be found in local courthouses, in local libraries, and in state government libraries. Local laws may also be accessed via the World Wide Web.
Avogadro's Law Meaning In Pakistan
Cross-references
Administrative Law and Procedure; Civil Law; Congress of the United States; Constitutional Amendment; Constitution of the United States; Court Opinion; Criminal Law; Equity; Federalism; Federal Register; Judicial Review; Private Law; Public Law; Stare Decisis.