What is the average molar mass of a mixture containing 3 mol of propane and 1 mol of hydrogen? The molar mass of C3H8 is 44.0 g/mol. the molar mass of H2 is 2.0 g/mol.
The correct answer and explanation is:
Let’s solve the problem step-by-step:
Problem Recap:
- You have a mixture with:
- 3 moles of propane (C₃H₈), molar mass = 44.0 g/mol
- 1 mole of hydrogen (H₂), molar mass = 2.0 g/mol
- You need to find the average molar mass of the mixture.
Step 1: Calculate total moles in the mixture
Total moles=3+1=4 moles\text{Total moles} = 3 + 1 = 4 \text{ moles}
Step 2: Calculate total mass of each component
- Mass of propane:
3 mol×44.0 g/mol=132.0 g3 \text{ mol} \times 44.0 \text{ g/mol} = 132.0 \text{ g}
- Mass of hydrogen:
1 mol×2.0 g/mol=2.0 g1 \text{ mol} \times 2.0 \text{ g/mol} = 2.0 \text{ g}
Step 3: Calculate total mass of the mixture
132.0 g+2.0 g=134.0 g132.0 \text{ g} + 2.0 \text{ g} = 134.0 \text{ g}
Step 4: Calculate average molar mass of the mixture
Average molar mass is total mass divided by total moles: Average molar mass=Total massTotal moles=134.0 g4 mol=33.5 g/mol\text{Average molar mass} = \frac{\text{Total mass}}{\text{Total moles}} = \frac{134.0 \text{ g}}{4 \text{ mol}} = 33.5 \text{ g/mol}
Final Answer:
33.5 g/mol\boxed{33.5 \text{ g/mol}}
Explanation (300 words):
The average molar mass of a mixture is the weighted average based on the amount (in moles) of each component and their respective molar masses. In this case, the mixture contains propane (C₃H₈) and hydrogen (H₂).
Propane has a molar mass of 44.0 g/mol, which means one mole of propane weighs 44.0 grams. Hydrogen gas, being much lighter, has a molar mass of only 2.0 g/mol. When combining different substances, the total mass is additive — the sum of each component’s mass. Similarly, the total moles is the sum of moles of each gas.
Since there are 3 moles of propane and 1 mole of hydrogen, the total moles are 4. The total mass is calculated by multiplying the moles of each gas by its molar mass and then summing:
- Propane contributes 3 moles × 44.0 g/mol = 132.0 g
- Hydrogen contributes 1 mole × 2.0 g/mol = 2.0 g
Adding these, the total mass of the mixture is 134.0 grams.
To find the average molar mass of the mixture, you divide the total mass by total moles: Average molar mass=134.0 g4 mol=33.5 g/mol\text{Average molar mass} = \frac{134.0 \text{ g}}{4 \text{ mol}} = 33.5 \text{ g/mol}
This value lies between the two molar masses and is closer to propane’s molar mass since propane is present in a greater amount. The average molar mass provides a meaningful single molar mass representing the entire mixture, useful in further calculations such as determining the mixture’s density, reaction stoichiometry, or other physical properties.