Chapter U3.64, Problem 6E

Interpretation Introduction

Interpretation: Whether10 mL of oxygen gas or 15 L of hydrogen gas has more particles 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 and T is temperature of the gas.

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

In 1 mol of any substance there are $6.022\times {10}^{23}$ units of substance are present. This is known as Avogadro’s number and represented by symbol $N_A$ .

Answer to Problem 6E

A balloon filled with 15 L of hydrogen gas has more particles than balloon filled with 10 L of oxygen gas.

Explanation of Solution

At STP, the temperature and pressure values are 273.15 K and 1 atm respectively. The volume of oxygen and hydrogen gas is given 10 L and 15 L respectively.

To calculate the number of particles of oxygen gas and hydrogen gas, number of moles of each needs to be calculated.

The ideal gas equation is represented as follows:

  $PV=nRT$

On rearranging,

  $n=\frac{PV}{RT}$

Putting the values to calculate the number of moles of oxygen gas,

  $n_{O_2}=\frac{\left(1\text{ atm}\right)\left(10\text{ L}\right)}{\left(0.082\text{ L atm/K mol}\right)\left(273.15\text{ K}\right)}=0.45\text{ mol}$

Similarly, the number of moles of hydrogen gas will be:

  $n_{H_2}=\frac{\left(1\text{ atm}\right)\left(15\text{ L}\right)}{\left(0.082\text{ L atm/K mol}\right)\left(273.15\text{ K}\right)}=0.67\text{ mol}$

The number of particles can be calculated using the Avogadro’s number as follows:

  $N_{O_2}=n_{O_2}{N}_A=0.45\text{ mol}\times \text{6}\text{.022}\times {\text{10}}^{23}{\text{ mol}}^{-1}=2.70\times {\text{10}}^{23}$

Similarly,

  $N_{H_2}=n_{H_2}{N}_A=0.67\text{ mol}\times \text{6}\text{.022}\times {\text{10}}^{23}{\text{ mol}}^{-1}=4.03\times {\text{10}}^{23}$

Thus, the number of particles of hydrogen gas is more than oxygen gas.

Conclusion

Thus, a balloon filled with 15 L of hydrogen gas has more particles than balloon filled with 10 L of oxygen gas.