A sample of a gas mixture contains 4.0 g of methane [tex] (CH_4) [/tex] and 2.0 g of helium (He).

What is the volume of the gas mixture at STP (273 K and 1.0 atm)? (molar volume at STP = 22.4 L)

A. 17 L
B. 130 L
C. 11 L
D. 5.6 L



Answer :

Sure, let's solve this problem step by step.

First, we need to determine the number of moles of each gas in the mixture.

### Step 1: Calculate the number of moles of each gas

Methane (CH₄):

1. Given mass of CH₄: 4.0 grams
2. Molar mass of CH₄: 16.04 g/mol

To find the number of moles of methane, we use the formula:

[tex]\[ \text{moles of CH₄} = \frac{\text{mass of CH₄}}{\text{molar mass of CH₄}} \][/tex]

[tex]\[ = \frac{4.0 \text{ grams}}{16.04 \text{ g/mol}} \approx 0.249 \text{ moles of CH₄} \][/tex]

Helium (He):

1. Given mass of He: 2.0 grams
2. Molar mass of He: 4.00 g/mol

To find the number of moles of helium, we use the formula:

[tex]\[ \text{moles of He} = \frac{\text{mass of He}}{\text{molar mass of He}} \][/tex]

[tex]\[ = \frac{2.0 \text{ grams}}{4.00 \text{ g/mol}} = 0.5 \text{ moles of He} \][/tex]

### Step 2: Calculate the total number of moles of the gas mixture

[tex]\[ \text{total moles} = \text{moles of CH₄} + \text{moles of He} \][/tex]

[tex]\[ = 0.249 \text{ moles of CH₄} + 0.5 \text{ moles of He} \approx 0.749 \text{ moles} \][/tex]

### Step 3: Determine the total volume of the gas mixture at STP

Given that at STP (273 K and 1.0 atm), one mole of any ideal gas occupies 22.4 liters, we can calculate the volume of the gas mixture using the formula:

[tex]\[ \text{volume at STP} = \text{total moles} \times \text{molar volume at STP} \][/tex]

[tex]\[ = 0.749 \text{ moles} \times 22.4 \text{ L/mol} \approx 16.786 \text{ L} \][/tex]

So, the volume of the gas mixture at STP is approximately 16.786 liters.

Therefore, the closest answer to the volume of the gas mixture at STP is 17 L.

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