Question

500 mL of nitrogen at 0.936 bar pressure and 1000 mL oxygen at 0.80 bar pressure are put together in a 2 L flask. If temperature is kept constant, calculate the final pressure of the mixture.

Answer 1

Hint: Pressure is the force applied perpendicular to the surface of an object. There are various units which are used to express pressure. The S.I unit of pressure is Pascal (Pa) and the C.G.S unit of pressure is $dyne/c{m^2}$. Pressure is also related with volume. The relation between pressure and volume is explained in Boyle’s Law.
This law states that – At constant temperature the volume of a given mass of a gas is inversely proportional to its pressure.
 Mathematically,
$V\alpha \dfrac{1}{P}$
$ \Rightarrow V = \dfrac{k}{P}$
$ \Rightarrow k = PV$ (where k is the proportionality constant)

Complete step by step answer:
In this numerical two gases are given which are put together in a 2 L flask and they mix up. So we will apply the Dalton’s Law of Partial Pressures which is the extension of Boyle’s Law.
 First we will find the partial pressure of nitrogen in the 2 L flask.
Given,
${P_1} = 0.936bar$
${V_1} = 500mL$
${V_2} = 2L = 2000mL$
Partial pressure of nitrogen is
\[\left( {{P_{Nitrogen}}} \right) = \dfrac{{{P_1}{V_1}}}{{{V_2}}}\]
\[ \Rightarrow \left( {{P_{Nitrogen}}} \right) = \dfrac{{0.936 \times 500}}{{2000}}\]
\[ \Rightarrow \left( {{P_{Nitrogen}}} \right) = \dfrac{{0.936}}{4}\]
\[ \Rightarrow \left( {{P_{Nitrogen}}} \right) = 0.234bar\]
 (After putting the given values in the formula we have calculated the partial pressure of nitrogen and is found to be 0.234 bar).
Now again we will calculate the partial pressure of oxygen in a 2 L flask.

Given,
${P_1} = 0.80bar$
${V_1} = 1000mL$
${V_2} = 2L = 2000mL$

Partial pressure of oxygen is
$\left( {{P_{oxygen}}} \right) = \dfrac{{{P_1}{V_1}}}{{{V_2}}}$
$ \Rightarrow \left( {{P_{oxygen}}} \right) = \dfrac{{0.80 \times 1000}}{{2000}}$
$ \Rightarrow \left( {{P_{oxygen}}} \right) = \dfrac{{0.80}}{2}$
$ \Rightarrow \left( {{P_{oxygen}}} \right) = 0.4bar$
(After putting the given values in the formula we have calculated the partial pressure of oxygen and is found to be 0.4 bar).

The total pressure of the mixture is
$ = {P_{Nitrogen}} + {P_{oxygen}}$
$ = (0.234 + 0.4)bar$
$ = 0.634bar$
(The final pressure will be the sum of the partial pressures of nitrogen and oxygen. So we put the values and calculated the total pressure of the mixture).

Therefore, the final pressure of the mixture is found to be 0.634 bar.

Note: Dalton’s law of partial pressure states that- When two or more chemically inert gases are enclosed in a vessel or allowed to intermix at constant temperature, the pressure exerted by the mixture of gases will be the sum of the partial pressures which each gas exerts when occupying the volume separately.