Chapter U3, Problem SII5RE

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 SII5RE

2.01 atm.

Explanation of Solution

Given Information: The initial volume, pressure and temperature of the gas is 7.5 L, 2.5 atm and 293 K respectively. Also, the volume and temperature after expansion is 10.0 L and 315 K respectively.

Calculation:

The ideal gas equation is as follows:

  $PV=nRT$

On rearranging, the number of moles of the air in the balloon can be calculated as follows:

  $n=\frac{P_1{V}_1}{R{T}_1}$

Putting the values,

  $n=\frac{\left(2.5\text{ atm}\right)\left(7.50\text{ L}\right)}{\left(0.082\text{ L atm/K mol}\right)\left(\text{293 K}\right)}=0.78\text{ mol}$

Thus, the number of moles of gas is 0.78. Since, the number of moles remains the same during expansion thus; new pressure can be calculated as follows:

  $P_2=\frac{nR{T}_2}{V_2}$

Putting the values,

  $\begin{array}{l}{P}_2=\frac{\left(0.78\text{ mol}\right)\left(0.082\text{ L atm/K mol}\right)\left(315K\right)}{\left(10.0\text{ L}\right)}\\ =2.01\text{ atm}\end{array}$

Conclusion

Thus, the new pressure of the gas is 2.01 atm.