A cylinder contains 40 g of HE, 56 g of N2, and 40 g of Ar. How many moles of each gas are in the mixture?
The correct answer and explanation is:
To determine the number of moles of each gas in the mixture, we use the formula: Moles=Mass (g)Molar Mass (g/mol)\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}
Step 1: Identify the molar mass of each gas:
- Helium (He): 4 g/mol
- Nitrogen (N₂): 28 g/mol
- Argon (Ar): 40 g/mol
Step 2: Calculate the moles of each gas:
1. Helium (He): 40 g4 g/mol=10 mol\frac{40\,g}{4\,g/mol} = 10\,\text{mol}
2. Nitrogen (N₂): 56 g28 g/mol=2 mol\frac{56\,g}{28\,g/mol} = 2\,\text{mol}
3. Argon (Ar): 40 g40 g/mol=1 mol\frac{40\,g}{40\,g/mol} = 1\,\text{mol}
Final Answer:
- He: 10 mol
- N₂: 2 mol
- Ar: 1 mol
300-Word Explanation:
To find the number of moles in a gas mixture, it’s essential to understand the concept of molar mass, which is the mass of one mole of a substance. The unit for molar mass is grams per mole (g/mol), and it varies depending on the type of gas.
In this case, we’re dealing with three gases: helium (He), nitrogen (N₂), and argon (Ar). Their molar masses are based on their atomic or molecular structure:
- Helium (He) is a noble gas and exists as a monoatomic gas with a molar mass of 4 g/mol.
- Nitrogen (N₂) exists as a diatomic molecule (two nitrogen atoms bonded together), giving it a molar mass of 28 g/mol (14 × 2).
- Argon (Ar) is also a noble gas, monoatomic, with a molar mass of 40 g/mol.
To find the number of moles of each gas, we divide the given mass by the molar mass:
- 40 grams of He divided by 4 g/mol equals 10 moles.
- 56 grams of N₂ divided by 28 g/mol equals 2 moles.
- 40 grams of Ar divided by 40 g/mol equals 1 mole.
Knowing the number of moles helps in many chemical calculations, including finding partial pressures, mole fractions, or total pressure in a gas mixture. These are all important in applications like gas laws (e.g., Dalton’s Law) and stoichiometry.