Questions: The molecular weight of a gas is A) 41 B) 2.7 × 10^-2 g / mol if 3.5 g of the gas occupies 2.1 L at STP. C) 4.6 × 10^2 D) 37 E) 5.5 × 10^3

Transcript text: The molecular weight of a gas is A) 41 B) $2.7 \times 10^{-2}$ $\mathrm{g} / \mathrm{mol}$ if 3.5 g of the gas occupies 2.1 L at STP. C) $4.6 \times 10^{2}$ D) 37 E) $5.5 \times 10^{3}$

Solution

Solution Steps

Step 1: Identify the given values and conditions

We are given:

Mass of the gas, $ m = 3.5 $ g
Volume of the gas, $ V = 2.1 $ L
Standard Temperature and Pressure (STP) conditions

Step 2: Recall the molar volume at STP

At STP, 1 mole of an ideal gas occupies 22.414 L.

Step 3: Calculate the number of moles of the gas

Using the molar volume at STP, we can find the number of moles $ n $ of the gas: \[ n = \frac{V}{22.414} = \frac{2.1 \, \text{L}}{22.414 \, \text{L/mol}} = 0.0937 \, \text{mol} \]

Step 4: Calculate the molecular weight of the gas

The molecular weight $ M $ is given by: \[ M = \frac{m}{n} = \frac{3.5 \, \text{g}}{0.0937 \, \text{mol}} = 37.35 \, \text{g/mol} \]

Step 5: Match the calculated molecular weight with the given options

The closest option to our calculated molecular weight is 37.