Chapter U3, Problem 11RE

Interpretation Introduction

Interpretation: The number of moles of hydrogen gas in the sample needs to be determined.

Concept Introduction:

The ideal gas equation is represented as follows:

  $PV=nRT$

Here, P is pressure, V is volume, n is number of moles, R is Universal gas constant and T is temperature of the gas.

Answer to Problem 11RE

12 mol.

Explanation of Solution

Given Information: The volume of hydrogen gas is 77.0 L, pressure is 3.5 atm and temperature is $2^o\text{C}$ .

Calculation:

First convert the given temperature to K as follows:

  $0{}^{\text{o}}\text{C}=\text{273}\text{.15 K}$

Thus,

  $2{}^{\text{o}}\text{C}=2+\text{273}\text{.15 K}=\text{275}\text{.15 K}$

The ideal gas equation is as follows:

  $PV=nRT$

On rearranging,

  $n=\frac{PV}{RT}$

Putting the values,

  $n=\frac{\left(3.5\text{ atm}\right)\left(77.0\text{ L}\right)}{\left(0.082\text{ L atm/K mol}\right)\left(275.15\text{ K}\right)}=12\text{ mol}$

Conclusion

Thus, the number of moles of hydrogen gas is 12 mol.