Question

an ideal gas occupies a volume of 1.0 cubic cm at 20 degrees and atmosphere . determine the number of molecules of gas in the container .(b) if the pressure of the 1.0-cm cubic volume is reduced to 1.0*10 to the power negative 11 Pa(an extremely good vacuum )while the temperature remains constant , how many moles of gas remain in the container ?

Answer 1

QUESTION:

an ideal gas occupies a volume of 1.0 cubic cm at 20 degrees and atmosphere.

(a) determine the number of molecules of gas in the container

(b) if the pressure of the 1.0-cm cubic volume is reduced to $1.0 \times 10^{-11} \, \text{Pa}$ (while the temperature remains constant, how many moles of gas remain in the container?

SOLUTION:

a) According to the ideal gas law

$$\begin{array}{l} p_1 V_1 = n_1 R T \\ n_1 = \frac{N_1}{N_A} \\ p_1 V_1 = \frac{N_1}{N_A} R T \\ N = \frac{p_1 V_1 N_A}{R T} = \frac{1.01 \cdot 10^5 \cdot 10^{-6} \cdot 6.02 \cdot 10^{23}}{8.31 \cdot (20 + 273)} = 2.5 \cdot 10^{19} \\ \end{array}$$

b) Analogically:

$$\begin{array}{l} p_2 V_1 = n_2 R T \\ n_2 = \frac{p_2 V_1}{R T} = \frac{10^{-11} \cdot 10^{-6}}{8.31 \cdot (20 + 273)} = 4.1 \cdot 10^{-21} \, \text{mol} \\ \end{array}$$

ANSWER

a) $2.5 \times 10^{19}$

b) $4.1 \times 10^{-21} \, \text{mol}$