Chapter U3, Problem 5RE

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 5RE

2.4 atm.

Explanation of Solution

Given Information:

The initial volume of gas and pressure is 2.5 L and 2 atm respectively. The final volume is 2.1 L and temperature remains the same.

Calculation:

The ideal gas equation is as follows:

  $PV=nRT$

It is given that temperature of the gas remains the same and number moles also remains the same. Thus, for constant temperature and number of moles, the relation between pressure and volume will be:

  $P_1{V}_1=P_2{V}_2$

On rearranging,

  $P_2=\frac{P_1{V}_1}{V_2}$

Putting the values,

  $\begin{array}{l}{P}_2=\frac{2\text{ atm}\times 2.5\text{ L}}{2.1\text{ L}}\\ =\text{2}\text{.4 atm}\end{array}$

Conclusion

Thus, the new pressure of the gas is 2.4 atm.