Chapter 13, Problem 6STP

Interpretation Introduction

Interpretation:

The unknown gas have to be identified.

Concept Introduction:

The ideal gas law was derived by combining three important laws of the gases. The ideal gas law can be expressed as-

  $\begin{array}{l}V\propto \frac{\mathrm{n}T}{P}\\ \mathrm{PV}=nRT\end{array}$ Where, R is universal gas constant.

The ideal gas law consists of all the variables of a gas such as pressure (P), volume (V), number of moles (n) and temperature (T).

Answer to Problem 6STP

This unknown gas is-

1. F₂.

Explanation of Solution

Data given: Mass of the gas = 4.37 gm

Pressure = 1.00 atm

Volume = 3.0 L

Temperature = 45 °C = (273 + 45) K = 318 K

R = 0.082 L atm/mol K

  $\begin{array}{l}PV=nRT\\ n=\frac{PV}{RT}\\ =\frac{1.00atm\times 3.0L}{0.082Latm/molK\times 318K}=0.115mol\end{array}$

Number of moles of the gas = 0.115 mol

Molecular weight of the unknown gas = $\frac{4.37gm}{0.115mol}=38gm/mol$

So, the unknown gas is F₂.

Conclusion

Reasons for incorrect options:

From the calculation we got the molecular weight of the unknown gas which is exact to the molecular weight of F₂.

So the answer is option A.

That means other options that is,

B. N₂

C. H₂

D. O₂ are found to be incorrect.