- The specific number of molecules in one gram- mole of a substance, defined as the molecular weight in grams, is 6.02214076 × 10 23, a quantity called Avogadro’s number, or the Avogadro constant.
- This is because Avogadro's law holds for all gases. The number of molecules in 1 mole of a gas is known to be 6.02 × 10 23, a value called Avogadro's number. As an example of the use of this important number, calculate the mass in grams of a single oxygen atom: 1 mole O 2 = 2(16.00) = 32.00 grams.
- The specific number of molecules in one gram- mole of a substance, defined as the molecular weight in grams, is 6.02214076 × 10 23, a quantity called Avogadro’s number, or the Avogadro constant.
Avogadro’s Law states that: 1 mole of every gas occupies the same volume, at the same temperature and pressure. At STP (standard temperature and pressure), this volume is 22.4 liters At RTP (room temperature and pressure), this volume is 24 dm 3 (liters).
A flat tire is not very useful. It does not cushion the rim of the wheel and creates a very uncomfortable ride. When air is added to the tire, the pressure increases as more molecules of gas are forced into the rigid tire. How much air should be put into a tire depends on the pressure rating for that tire. Too little pressure and the tire will not hold its shape. Too much pressure and the tire could burst.
Avogadro's Law
You have learned about Avogadro's hypothesis: equal volumes of any gas at the same temperature and pressure contain the same number of molecules. It follows that the volume of a gas is directly proportional to the number of moles of gas present in the sample. Avogadro's Law states that the volume of a gas is directly proportional to the number of moles (or number of particles) of gas when the temperature and pressure are held constant. The mathematical expression of Avogadro's Law is:
[V = k times n]
or
[dfrac{V_1}{n_1} = dfrac{V_2}{n_2}]
where (n) is the number of moles of gas and (k) is a constant. Avogadro's Law is in evidence whenever you blow up a balloon. The volume of the balloon increases as you add moles of gas to the balloon by blowing it up.
If the container holding the gas is rigid rather than flexible, pressure can be substituted for volume in Avogadro's Law. Adding gas to a rigid container makes the pressure increase.
Example (PageIndex{1})
A balloon has been filled to a volume of (1.90 : text{L}) with (0.0920 : text{mol}) of helium gas. If (0.0210 : text{mol}) of additional helium is added to the balloon while the temperature and pressure are held constant, what is the new volume of the balloon?
/Avogadro-58f7d6f35f9b581d5983024e.jpg "Avogadro")
Solution
Steps for Problem Solving | |
|---|---|
| Identify the 'given' information and what the problem is asking you to 'find.' | Given: (V_1 = 1.90 : text{L}) (n_1 = 0.0920 : text{mol}) Find: (V_2 = ? : text{L}) |
| List other known quantities. | Note that the final number of moles has to be calculated by adding the original number of moles to the moles of added helium. (n_2 = 0.0920 + 0.0210 = 0.1130 : text{mol}) |
Plan the problem. | First, rearrange the equation algebraically to solve for (V_2). [V_2 = frac{V_1 times n_2}{n_1}] |
Calculate. | Now substitute the known quantities into the equation and solve. [V_2 = frac{1.90 : text{L} times 0.1130 : cancel{text{mol}}}{0.0920 : cancel{text{mol}}} = 2.33 : text{L}] |
| Think about your result. | Since a relatively small amount of additional helium was added to the balloon, its volume increases slightly. |
Exercise (PageIndex{1})
A 12.8 L volume of gas contains .000498 moles of oxygen gas. At constant temperature and pressure, what volume does .0000136 moles of the gas fill?
0.350 L
Summary
- Calculations for relationships between volume and number of moles of a gas can be performed using Avogadro's Law.
Contributions & Attributions
This page was constructed from content via the following contributor(s) and edited (topically or extensively) by the LibreTexts development team to meet platform style, presentation, and quality:
CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon.
Marisa Alviar-Agnew (Sacramento City College)
Henry Agnew (UC Davis)
A flat tire is not very useful. It does not cushion the rim of the wheel and creates a very uncomfortable ride. When air is added to the tire, the pressure increases as more molecules of gas are forced into the rigid tire. How much air should be put into a tire depends on the pressure rating for that tire. Too little pressure and the tire will not hold its shape. Too much pressure and the tire could burst.
Avogadro's Law
You have learned about Avogadro's hypothesis: equal volumes of any gas at the same temperature and pressure contain the same number of molecules. It follows that the volume of a gas is directly proportional to the number of moles of gas present in the sample. Avogadro's Law states that the volume of a gas is directly proportional to the number of moles (or number of particles) of gas when the temperature and pressure are held constant. The mathematical expression of Avogadro's Law is:
[V = k times n]
or Don%27t starve together mac free for mac.
[dfrac{V_1}{n_1} = dfrac{V_2}{n_2}]
where (n) is the number of moles of gas and (k) is a constant. Avogadro's Law is in evidence whenever you blow up a balloon. The volume of the balloon increases as you add moles of gas to the balloon by blowing it up.
If the container holding the gas is rigid rather than flexible, pressure can be substituted for volume in Avogadro's Law. Adding gas to a rigid container makes the pressure increase.
Example (PageIndex{1})
Formula Avogadro's Number
A balloon has been filled to a volume of (1.90 : text{L}) with (0.0920 : text{mol}) of helium gas. If (0.0210 : text{mol}) of additional helium is added to the balloon while the temperature and pressure are held constant, what is the new volume of the balloon?
Avogadro's Law Number 3
Solution
Steps for Problem Solving | |
|---|---|
| Identify the 'given' information and what the problem is asking you to 'find.' | Given: (V_1 = 1.90 : text{L}) (n_1 = 0.0920 : text{mol}) Find: (V_2 = ? : text{L}) |
| List other known quantities. | Note that the final number of moles has to be calculated by adding the original number of moles to the moles of added helium. (n_2 = 0.0920 + 0.0210 = 0.1130 : text{mol}) |
Plan the problem. | First, rearrange the equation algebraically to solve for (V_2). [V_2 = frac{V_1 times n_2}{n_1}] |
Calculate. | Now substitute the known quantities into the equation and solve. [V_2 = frac{1.90 : text{L} times 0.1130 : cancel{text{mol}}}{0.0920 : cancel{text{mol}}} = 2.33 : text{L}] |
| Think about your result. | Since a relatively small amount of additional helium was added to the balloon, its volume increases slightly. |
Exercise (PageIndex{1})
A 12.8 L volume of gas contains .000498 moles of oxygen gas. At constant temperature and pressure, what volume does .0000136 moles of the gas fill?
0.350 L
Avogadro's Law Number 8
Summary
- Calculations for relationships between volume and number of moles of a gas can be performed using Avogadro's Law.
Contributions & Attributions
This page was constructed from content via the following contributor(s) and edited (topically or extensively) by the LibreTexts development team to meet platform style, presentation, and quality:
CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon.
Marisa Alviar-Agnew (Sacramento City College)
Henry Agnew (UC Davis)