Chapter U3, Problem SII4RE

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 SII4RE

  $3.86\text{ atm}$ .

Explanation of Solution

Given Information:

The initial pressure and temperature of the gas sample in rigid container is 3.0 atm and 350 K respectively. Also, the final temperature is 450 K.

Calculation:

The ideal gas equation is as follows:

  $PV=nRT$

For the given gas sample, pressure and temperature are changing at constant volume and number of moles as gas is present in a rigid container thus,

  $\frac{P_1}{T_1}=\frac{P_2}{T_2}$

On rearranging,

  $P_2=\frac{P_1}{T_1}{T}_2$

Putting the values,

  $P_2=\left(\frac{3.0\text{ atm}}{350\text{ K}}\right)\left(450\text{ K}\right)=3.86\text{ atm}$

Conclusion

Thus, the new pressure of the gas is $3.86\text{ atm}$ .