Question
Model Molar Mass and Molar Volume
Remember that the mole is called the chemist’s dozen and is used for atoms, molecules, or other small particles. Follow these steps to measure the mass of elements using the concept of molar mass and the volume of a gas sample of an element using the concept of molar volume.
Develop and Use Your Model
1. SEP Using Mathematics and Computational Thinking Using the data listed in the table, plot a graph to show the mass of a gas sample versus moles of the gas. Use graphing software or draw the graph. For each of the elements, connect the three points with a straight line. Use different dot shapes or colors to distinguish the three gases. Label each line you draw.
Masses and Volumes for Gas Samples
Sample Gas Moles Mass (g) Volume (L, at STP)
1 Oxygen (O2) 0.5 16.0 11.2
2 Oxygen (O2) 1 32.0 22.4
3 Oxygen (O2) 2 64.0 44.8
4 Hydrogen (H2) 1 2.0 22.4
5 Hydrogen (H2) 3 6.0 67.2
6 Hydrogen (H2) 6 12.0 134.4
7 Neon (Ne) 0.5 10.1 11.2
8 Neon (Ne) 2 40.4 44.8
9 Neon (Ne) 4 80.8 89.6
Graph of Mass vs. Moles
2. SEP Use Models The slope of a line is equal to the rise, or distance in y-values, divided by the run, or distance in x-values. Calculate the slope of the line for each gas. Use the formula for the slope:
Oxygen (O2):
Hydrogen (H2):
Neon (Ne):
3. SEP Interpret Data How does the slope of the line relate to the masses of the samples of each element? (Hint: The unit for the slope is the unit of the y-axis, or mass, divided by the unit of the x-axis, or moles.)
Evaluate and Revise Your Model
4. SEP Use Math Use a pencil and ruler to graph in the space or use graphing software to plot the volume of a gas versus the number of moles of the gas, as shown in the data table. Be sure to use different dot shapes or colors for each gas and to label the lines.
5. SEP Synthesize Information What does the graph show about the molar volume of a gas? How is molar volume different from molar mass?
6. SEP Synthesize Information You have a sample of 0.25 mol of an unknown gas at STP. Can you predict the volume of the gas, even if you do not know the identity of the gas? Can you predict the mass of the sample? Explain.
Remember that the mole is called the chemist’s dozen and is used for atoms, molecules, or other small particles. Follow these steps to measure the mass of elements using the concept of molar mass and the volume of a gas sample of an element using the concept of molar volume.
Develop and Use Your Model
1. SEP Using Mathematics and Computational Thinking Using the data listed in the table, plot a graph to show the mass of a gas sample versus moles of the gas. Use graphing software or draw the graph. For each of the elements, connect the three points with a straight line. Use different dot shapes or colors to distinguish the three gases. Label each line you draw.
Masses and Volumes for Gas Samples
Sample Gas Moles Mass (g) Volume (L, at STP)
1 Oxygen (O2) 0.5 16.0 11.2
2 Oxygen (O2) 1 32.0 22.4
3 Oxygen (O2) 2 64.0 44.8
4 Hydrogen (H2) 1 2.0 22.4
5 Hydrogen (H2) 3 6.0 67.2
6 Hydrogen (H2) 6 12.0 134.4
7 Neon (Ne) 0.5 10.1 11.2
8 Neon (Ne) 2 40.4 44.8
9 Neon (Ne) 4 80.8 89.6
Graph of Mass vs. Moles
2. SEP Use Models The slope of a line is equal to the rise, or distance in y-values, divided by the run, or distance in x-values. Calculate the slope of the line for each gas. Use the formula for the slope:
Oxygen (O2):
Hydrogen (H2):
Neon (Ne):
3. SEP Interpret Data How does the slope of the line relate to the masses of the samples of each element? (Hint: The unit for the slope is the unit of the y-axis, or mass, divided by the unit of the x-axis, or moles.)
Evaluate and Revise Your Model
4. SEP Use Math Use a pencil and ruler to graph in the space or use graphing software to plot the volume of a gas versus the number of moles of the gas, as shown in the data table. Be sure to use different dot shapes or colors for each gas and to label the lines.
5. SEP Synthesize Information What does the graph show about the molar volume of a gas? How is molar volume different from molar mass?
6. SEP Synthesize Information You have a sample of 0.25 mol of an unknown gas at STP. Can you predict the volume of the gas, even if you do not know the identity of the gas? Can you predict the mass of the sample? Explain.
Answers
GPT-4o mini
### Develop and Use Your Model
1. **Graph of Mass vs. Moles**:
Given the provided data, we can plot the mass of each gas sample against the number of moles of the gas:
| Gas | Moles | Mass (g) |
|----------|-------|----------|
| O2 | 0.5 | 16.0 |
| O2 | 1 | 32.0 |
| O2 | 2 | 64.0 |
| H2 | 1 | 2.0 |
| H2 | 3 | 6.0 |
| H2 | 6 | 12.0 |
| Ne | 0.5 | 10.1 |
| Ne | 2 | 40.4 |
| Ne | 4 | 80.8 |
Using graphing software or manually plotting this data, you should obtain three lines representing the mass of O2, H2, and Ne. Make sure to differentiate the lines using colors or dot shapes.
2. **Slope Calculation**:
To calculate the slope of the line for each gas, we can use the formula:
\[
\text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{\Delta \text{Mass}}{\Delta \text{Moles}}
\]
- **Oxygen (O2)**:
- From (0.5 moles, 16.0 g) to (2 moles, 64.0 g):
\[
\text{Slope (O2)} = \frac{64.0 - 16.0}{2 - 0.5} = \frac{48.0}{1.5} = 32.0 \text{ g/mol}
\]
- **Hydrogen (H2)**:
- From (1 mole, 2.0 g) to (6 moles, 12.0 g):
\[
\text{Slope (H2)} = \frac{12.0 - 2.0}{6 - 1} = \frac{10.0}{5} = 2.0 \text{ g/mol}
\]
- **Neon (Ne)**:
- From (0.5 moles, 10.1 g) to (4 moles, 80.8 g):
\[
\text{Slope (Ne)} = \frac{80.8 - 10.1}{4 - 0.5} = \frac{70.7}{3.5} = 20.2 \text{ g/mol}
\]
3. **Interpretation of Data**:
The slope of each gas line represents the molar mass of that gas, as it expresses the mass (in grams) per mole of that gas. Therefore:
- The slope for O2 is 32.0 g/mol, indicating that 1 mole of oxygen gas has a mass of 32.0 grams.
- The slope for H2 is 2.0 g/mol, indicating that 1 mole of hydrogen gas has a mass of 2.0 grams.
- The slope for Ne is 20.2 g/mol, indicating that 1 mole of neon gas has a mass of 20.2 grams.
### Evaluate and Revise Your Model
4. **Graph of Volume vs. Moles**:
With the same data, you can plot the volume of each gas sample against the number of moles:
| Gas | Moles | Volume (L) |
|----------|-------|------------|
| O2 | 0.5 | 11.2 |
| O2 | 1 | 22.4 |
| O2 | 2 | 44.8 |
| H2 | 1 | 22.4 |
| H2 | 3 | 67.2 |
| H2 | 6 | 134.4 |
| Ne | 0.5 | 11.2 |
| Ne | 2 | 44.8 |
| Ne | 4 | 89.6 |
Again, use graphing software or plot this data manually.
5. **Interpretation of Molar Volume**:
The graph will show that the volume of a gas increases linearly with the number of moles at standard temperature and pressure (STP). It indicates that one mole of gas occupies roughly the same volume (22.4 L) at STP, irrespective of the type of gas.
**Difference between Molar Volume and Molar Mass**:
- **Molar mass** is the mass of one mole of a substance (in g/mol), describing how much matter is in that mole.
- **Molar volume** is the volume that one mole of gas occupies at STP (in L/mol), describing the space that mole occupies.
6. **Predicting Volume and Mass of Unknown Gas**:
Yes, even if the identity of the gas is unknown, you can predict its volume and mass at STP using the known molar volume of gases. At STP, 1 mole of any ideal gas occupies 22.4 liters.
- **Volume**: For 0.25 moles:
\[
\text{Volume} = 0.25 \text{ moles} \times 22.4 \text{ L/mol} = 5.6 \text{ L}
\]
- **Mass**: If you knew the molar mass of the unknown gas, you could estimate the mass. However, without the gas’s identity, you cannot calculate the mass accurately. If, hypothetically, the unknown gas had a molar mass similar to air (about 29 g/mol), for example, you could estimate:
\[
\text{Mass} = 0.25 \text{ moles} \times 29 \text{ g/mol} = 7.25 \text{ g}
\]
In summary, while you can predict the volume at STP accurately, the mass prediction requires knowledge of the gas's molar mass.
1. **Graph of Mass vs. Moles**:
Given the provided data, we can plot the mass of each gas sample against the number of moles of the gas:
| Gas | Moles | Mass (g) |
|----------|-------|----------|
| O2 | 0.5 | 16.0 |
| O2 | 1 | 32.0 |
| O2 | 2 | 64.0 |
| H2 | 1 | 2.0 |
| H2 | 3 | 6.0 |
| H2 | 6 | 12.0 |
| Ne | 0.5 | 10.1 |
| Ne | 2 | 40.4 |
| Ne | 4 | 80.8 |
Using graphing software or manually plotting this data, you should obtain three lines representing the mass of O2, H2, and Ne. Make sure to differentiate the lines using colors or dot shapes.
2. **Slope Calculation**:
To calculate the slope of the line for each gas, we can use the formula:
\[
\text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{\Delta \text{Mass}}{\Delta \text{Moles}}
\]
- **Oxygen (O2)**:
- From (0.5 moles, 16.0 g) to (2 moles, 64.0 g):
\[
\text{Slope (O2)} = \frac{64.0 - 16.0}{2 - 0.5} = \frac{48.0}{1.5} = 32.0 \text{ g/mol}
\]
- **Hydrogen (H2)**:
- From (1 mole, 2.0 g) to (6 moles, 12.0 g):
\[
\text{Slope (H2)} = \frac{12.0 - 2.0}{6 - 1} = \frac{10.0}{5} = 2.0 \text{ g/mol}
\]
- **Neon (Ne)**:
- From (0.5 moles, 10.1 g) to (4 moles, 80.8 g):
\[
\text{Slope (Ne)} = \frac{80.8 - 10.1}{4 - 0.5} = \frac{70.7}{3.5} = 20.2 \text{ g/mol}
\]
3. **Interpretation of Data**:
The slope of each gas line represents the molar mass of that gas, as it expresses the mass (in grams) per mole of that gas. Therefore:
- The slope for O2 is 32.0 g/mol, indicating that 1 mole of oxygen gas has a mass of 32.0 grams.
- The slope for H2 is 2.0 g/mol, indicating that 1 mole of hydrogen gas has a mass of 2.0 grams.
- The slope for Ne is 20.2 g/mol, indicating that 1 mole of neon gas has a mass of 20.2 grams.
### Evaluate and Revise Your Model
4. **Graph of Volume vs. Moles**:
With the same data, you can plot the volume of each gas sample against the number of moles:
| Gas | Moles | Volume (L) |
|----------|-------|------------|
| O2 | 0.5 | 11.2 |
| O2 | 1 | 22.4 |
| O2 | 2 | 44.8 |
| H2 | 1 | 22.4 |
| H2 | 3 | 67.2 |
| H2 | 6 | 134.4 |
| Ne | 0.5 | 11.2 |
| Ne | 2 | 44.8 |
| Ne | 4 | 89.6 |
Again, use graphing software or plot this data manually.
5. **Interpretation of Molar Volume**:
The graph will show that the volume of a gas increases linearly with the number of moles at standard temperature and pressure (STP). It indicates that one mole of gas occupies roughly the same volume (22.4 L) at STP, irrespective of the type of gas.
**Difference between Molar Volume and Molar Mass**:
- **Molar mass** is the mass of one mole of a substance (in g/mol), describing how much matter is in that mole.
- **Molar volume** is the volume that one mole of gas occupies at STP (in L/mol), describing the space that mole occupies.
6. **Predicting Volume and Mass of Unknown Gas**:
Yes, even if the identity of the gas is unknown, you can predict its volume and mass at STP using the known molar volume of gases. At STP, 1 mole of any ideal gas occupies 22.4 liters.
- **Volume**: For 0.25 moles:
\[
\text{Volume} = 0.25 \text{ moles} \times 22.4 \text{ L/mol} = 5.6 \text{ L}
\]
- **Mass**: If you knew the molar mass of the unknown gas, you could estimate the mass. However, without the gas’s identity, you cannot calculate the mass accurately. If, hypothetically, the unknown gas had a molar mass similar to air (about 29 g/mol), for example, you could estimate:
\[
\text{Mass} = 0.25 \text{ moles} \times 29 \text{ g/mol} = 7.25 \text{ g}
\]
In summary, while you can predict the volume at STP accurately, the mass prediction requires knowledge of the gas's molar mass.