Question

For 400cc of ${N_2}$, at 600mm and 500cc of $O_2$, at 300 mm are quantitatively transferred into an empty vessel of ${\text{2 L}}$ capacity. Calculate the pressure of the mixture and partial pressure of the final mixture.

Answer 1

Hint: The term cc is also taken as mL. The mixture of two gases is given and values of volume and pressure are given. There is a need to calculate the final pressure of the mixture and one can do that by calculating the formula as the addition of two terms of gases is equal to the mixture.

Complete step by step answer:
1) First of all we will see what data has been given in the question as below,
The volume of nitrogen gas $\left( {{V_1}} \right) = 400mL$
The pressure of nitrogen gas \[\left( {{P_1}} \right) = 600mm\]
The volume of oxygen gas $\left( {{V_1}} \right) = 500mL$
The pressure of oxygen gas $\left( {{P_2}} \right) = 300mm$
Volume of mixture ${V_{mix}} = 2L = 2000mL$
Pressure of mixture ${P_{mix}} = ?$
2) Now let us see the formula by which we can calculate the pressure of mixture as below,
${P_1}{V_1} + {P_2}{V_2} = {P_{mix}}{V_{mix}}$
In the above equation, the nitrogen gas and oxygen gas are mixed together to form the mixture.
Now let us put the values in the above equation as below,
$400 \times 600 + 500 \times 300 = {P_{mix}} \times 2000$
3) Now let us calculate the multiplication part as below,
$240000 + 150000 = {P_{mix}} \times 2000$
Now let us calculate the addition part we get,
$390000 = {P_{mix}} \times 2000$
4) Now as we need to calculate the value of ${P_{mix}}$ we can do that by taking that value to one side and we get the equation as below,
${P_{mix}} = \dfrac{{390000}}{{2000}}$
Now let us calculate the divide part and we get the value as below,
${P_{mix}} = 195mm$
Therefore, the pressure of the final mixture will be ${\text{195mm}}$.

Note:
The total pressure of the mixture can be calculated as the sum of the partial pressure of all the gases that are mixed together to form the mixture. Partial pressure can be elaborated as the pressure exerted by an individual gas in a mixture.