Questions: A 2.70-g sample of a gas occupies 15.0 L at 2.00 atm and 273 K. What is the molar mass of the gas? Molar mass = g / mol

A 2.70-g sample of a gas occupies 15.0 L at 2.00 atm and 273 K. What is the molar mass of the gas? Molar mass = g / mol
Transcript text: A 2.70-g sample of a gas occupies 15.0 L at 2.00 atm and 273 K . What is the molar mass of the gas? Molar mass = $\square$ $\mathrm{g} / \mathrm{mol}$ Submit Answer Try Another Version 1 item attempt remaining
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Solution

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Solution Steps

Step 1: Identify the Given Variables

We are given the following information:

  • Mass of the gas, \( m = 2.70 \) g
  • Volume of the gas, \( V = 15.0 \) L
  • Pressure of the gas, \( P = 2.00 \) atm
  • Temperature of the gas, \( T = 273 \) K
Step 2: Use the Ideal Gas Law

The ideal gas law is given by: \[ PV = nRT \] where:

  • \( P \) is the pressure
  • \( V \) is the volume
  • \( n \) is the number of moles
  • \( R \) is the ideal gas constant (\( R = 0.0821 \) L·atm/(mol·K))
  • \( T \) is the temperature
Step 3: Solve for the Number of Moles

Rearrange the ideal gas law to solve for \( n \): \[ n = \frac{PV}{RT} \]

Substitute the given values: \[ n = \frac{(2.00 \, \text{atm})(15.0 \, \text{L})}{(0.0821 \, \text{L·atm/(mol·K)})(273 \, \text{K})} \]

Calculate \( n \): \[ n = \frac{30.0}{22.4133} \approx 1.338 \, \text{mol} \]

Step 4: Calculate the Molar Mass

The molar mass \( M \) is given by: \[ M = \frac{m}{n} \]

Substitute the values for \( m \) and \( n \): \[ M = \frac{2.70 \, \text{g}}{1.338 \, \text{mol}} \approx 2.018 \, \text{g/mol} \]

Final Answer

The molar mass of the gas is: \[ \boxed{2.018 \, \text{g/mol}} \]

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