Question

4 gram oxygen and 2 gram hydrogen are kept in a one-litre container at ${{0}^{0}}C$ . Calculate the total pressure.

Answer 1

The ideal gas law (PV= nRT) can be used to find the value of total pressure of the container. The number of moles of both hydrogen and oxygen need to be found and added to get the total number of moles in the container.

Formula used: The number of moles can be found using the equation –
$\text{Number of Moles=}\dfrac{\text{ Given Mass}}{\text{Molar Mass}}$

Complete step by step solution:
In order to calculate the total pressure of the container, we can use the ideal gas law (PV = nRT).
We have to find the total pressure (P) of the container. Hence, it is necessary that we find the total number of moles in the container. So, we have to find the number of moles of both hydrogen and oxygen and then add them to get the total number of moles in the container.
For calculating the number of moles of hydrogen and oxygen, we can use the equation-

$\text{Number of Moles=}\dfrac{\text{ Given Mass}}{\text{Molar Mass}}$

Hence, the number of moles of hydrogen and oxygen will be –
Number of moles of oxygen (${{O}_{2}}$) = $\dfrac{4}{32}$= 0.125 moles

Number of moles of hydrogen (${{H}_{2}}$) = $\dfrac{2}{2}$ = 1 mole
Therefore, the total number of moles (n) will be 1 + 0.125 = 1.125
We know that the volume of the container (V) is 1 L, and the temperature (T) is ${{0}^{0}}C$, that is T = 273 K. We also know that the value of R in terms of L and atm is, R = 0.0821 L atm / mol K.
Substituting the values of V, n, R, T in the ideal gas law, we get the total pressure, P as –

$\text{P=}\dfrac{\text{nRT}}{\text{V}}=\dfrac{1.125\text{ $\times$ 0}\text{.0821 $\times$ 273}}{1}=25.21\text{ atm}$

Note: It is important that you convert the temperature from degree celsius to kelvin. This is because the Kelvin scale is the SI unit of temperature. Using the value of zero degree celsius will give you the value of pressure to be 0, which is incorrect.