Chapter U3.17, Problem 6E

Interpretation Introduction

Interpretation: The number of moles of helium needs to be determined which is required to fill in the 10000 L balloon at 1 atm and 10 ^oC.

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 6E

  $430.7\text{ mol}$

Explanation of Solution

The ideal gas equation is represented as follows:

  $PV=nRT$

On rearranging,

  $n=\frac{PV}{RT}$

First convert temperature from ^oC to K as follows:

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

Thus,

  $10{}^{\text{o}}\text{C=}\left(\text{10+273}\text{.15}\right)\text{ K=283}\text{.15 K}$

Putting the values to calculate the number of moles of gas as follows:

  $n=\frac{\left(1\text{ atm}\right)\left(10000\text{ L}\right)}{\left(0.082\text{ L atm/K mol}\right)\left(283.15\text{ K}\right)}=430.7\text{ mol}$

Conclusion

Thus, number of moles of helium gas is $430.7\text{ mol}$ .