Question

What will be the pressure exerted by a mixture of $3.2g$ of methane and $4.4g$ of carbon dioxide contained in $9d{m^3}$ flask at $27^\circ C$?

Answer 1

Hint: For this question, we will be using the ideal gas equation. The equation of state of a hypothetical ideal gas is known as the ideal gas law. Although it has significant drawbacks, it is a good approximation to the behaviour of various gases under many conditions. The ideal gas law describes the behaviour of an ideal sample of gas, and how that behaviour is related to the pressure (P), temperature (T), volume (V), and molarity (n) of the gas sample.

Complete answer:
We know that the ideal gas equation is given by
\[{\text{PV = nRT}}\]
Where,
\[{\text{P}}\]is the pressure of the ideal gas.
\[{\text{V}}\]is the volume of the ideal gas.
\[{\text{n}}\]is the amount of ideal gas measured in terms of moles.
\[{\text{R}}\]is the universal gas constant.
\[{\text{T}}\] is the temperature.
We know that, molecular weight of methane \[{\text{ = 16g}}\]
Thus, \[{\text{3}}{\text{.2g}}\] of methane will be \[\dfrac{{{\text{3}}{\text{.2}}}}{{{\text{16}}}}{\text{moles}}\] \[{\text{ = }}\] \[{\text{0}}{\text{.2moles}}\]
The pressure exerted by methane is given by
\[P = \dfrac{{nRT}}{V} = \dfrac{{0.2 \times 8.314 \times 300}}{{9 \times {{10}^3}}}\]
On simplification we get,
$ = 5.54 \times {10^4}Pa$
Similarly, molecular weight of carbon dioxide \[ = 44g\]
Thus, \[{\text{4}}{\text{.4g}}\]of carbon dioxide will be \[\dfrac{{4.4}}{{44}} = 0.1moles\]
The pressure exerted by carbon dioxide is given by,
\[P = \dfrac{{nRT}}{V} = \dfrac{{0.1 \times 8.314 \times 300}}{{9 \times {{10}^{ - 3}}}} = 2.77 \times {10^4}Pa\]
Thus, the total pressure will be given by the sum of the pressure exerted by methane and the pressure exerted by carbon dioxide.
$Total pressure = 5.54 \times {10^4}Pa + 2.77 \times {10^4}Pa$
On simplification we get,
$ = 8.31 \times {10^4}Pa$
We must be aware that the value of \[R = 8.314J/K/mol\] and
\[T = 27^\circ C = 300K\]
Thus, the pressure exerted by a mixture of \[3.2g\] of methane and \[4.4g\] of carbon dioxide contained in \[9d{m^3}\] flask at $27^\circ C$ is $ = 8.31 \times {10^4}Pa$.

Note:
We must note that the ideal gas law is a well-defined approximation of the behaviour of several gases under various situations in thermodynamics. The Ideal Gas Equation combines empirical laws such as Charle's law, Boyle's law, Gay-law, Lussac's and Avogadro's law into one equation. The Ideal Gas Equation is a mathematical expression of the states of hypothetical gases using a combination of empirical and physical constants. The general gas equation is another name for it.