Chapter U3, Problem SII3RE

Interpretation Introduction

Interpretation: The new pressure of the gas 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 SII3RE

  $0.795\text{ atm}$ .

Explanation of Solution

Given Information:

The initial volume and pressure of the gas is 26.5 L and 1.5 atm respectively. The final volume of the gas is 50.0 L at constant temperature.

Calculation:

The ideal gas equation is as follows:

  $PV=nRT$

On expansion, number of moles of the gas also remains the same. Thus, at constant temperature and number of moles,

  $P_1{V}_1=P_2{V}_2$

On rearranging,

  $P_2=\frac{P_1{V}_1}{V_2}$

Putting the values,

  $P_2=\frac{\left(1.5\text{ atm}\right)\left(26.5\text{ L}\right)}{\left(50.0\text{ L}\right)}=0.795\text{ atm}$

Conclusion

Thus, the new pressure of the gas is $0.795\text{ atm}$ .