Question

use the following information to answer the next question.
a scientist isolates 2.366 g of gas. the sample occupies a volume of 800 ml at 78.0°c and 103 kpa. the scientist uses this data to calculate the molar mass and thus identify the gas.

1. the gas the scientist isolated was

xe
f₂
br₂
kr

Explanation:

Step1: Convert units

• Convert temperature from Celsius to Kelvin: \(T=(78.0 + 273.15)\text{K}=351.15\text{K}\)
• Convert volume from mL to L: \(V = 800\text{mL}=0.8\text{L}\)
• Use the ideal gas law \(PV=nRT\), where \(P = 103\text{kPa}\), \(R=8.314\text{J/(mol}\cdot\text{K)}\) (since \(1\text{kPa}\cdot\text{L}=1\text{J}\))
• Rearrange for \(n\): \(n=\frac{PV}{RT}\)

$$n=\frac{103\times0.8}{8.314\times351.15}$$

$$n=\frac{82.4}{2920.0}$$

$$n\approx0.0282\text{mol}$$

Step2: Calculate molar mass

• Molar mass \(M=\frac{m}{n}\), where \(m = 2.366\text{g}\)

$$M=\frac{2.366}{0.0282}$$

$$M\approx84\text{g/mol}$$

Answer:

Kr (since the molar mass of Kr is approximately \(83.8\text{g/mol}\))