Chapter U3.65, Problem 5E

Interpretation Introduction

Interpretation: The pressure of the gas needs to be calculated, if number of moles of gas is 3.40 mol, temperature is 40 ^oC and volume is 22.4 L.

Concept Introduction: The ideal gas equation is represented as follows:

  $PV=nRT$

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

R is Universal gas constant with value $0.082\text{ L atm/K mol}$ .

Answer to Problem 5E

3.9 atm.

Explanation of Solution

The number of moles of gas is 3.40 mol, temperature is 40 ^oC and volume is 22.4 L.

The ideal gas equation is represented as follows:

  $PV=nRT$

On rearranging,

  $P=\frac{nRT}{V}$

First convert temperature from ^oC to K as follows:

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

Thus,

  $40{}^{\text{o}}\text{C=}\left(\text{40+273}\text{.15}\right)\text{ K=313}\text{.15 K}$

Putting the values to calculate the pressure of gas as follows:

  $P=\frac{\left(3.40\text{ mol}\right)\left(0.082\text{ L atm/K mol}\right)\left(313.15\text{ K}\right)}{\left(22.4\text{ L}\right)}=3.9\text{ atm}$

Conclusion

Thus, the pressure of the gas is 3.9 atm.