Question

Calculate the total pressure in a mixture of ${ 8g }$ of dioxygen and ${ 4g }$ of dihydrogen confined in a vessel of ${ 1dm }^{ 3 }$ at${ 27 }^{ \circ }{ C }$.
 ${ R=0.083bardm }^{ 3 }{ K }^{ -1 }{ mol }^{ -1 }$.

Answer 1

Hint: Ideal gases are those gases that obey the ideal gas equation ( PV= nRT ) or gas laws under all conditions of temperature and pressure.

Complete answer:
It is given that,
Mass of oxygen = ${ 8g }$
The molar mass of oxygen = ${ 32g/mol }$
Mass of hydrogen = ${ 4g }$
Temperature = ${ 27 }^{ \circ }{ C }$ = ${ (27+273) = 300K }$
 ${ R=0.083bardm }^{ 3 }{ K }^{ -1 }{ mol }^{ -1 }$.
The molar mass of hydrogen = ${ 2g/mol }$
As we know, the Number of moles = ${ mass\div molar\quad mass }$
Therefore, the amount of oxygen = ${ 8\div 32=0.25mol }$
The amount of hydrogen = ${ 4\div 2=2mol }$
According to the ideal gas equation, PV=nRT ………(1)
where P = pressure
V = volume
n = number of moles
R = Universal gas constant
T = temperature
Now, put the values in equation (1), we get
P(1) = ${ 0.25+2\times 0.083\times 300 }$
P = ${ 2.25\times 0.083\times 300 }$
P = ${ 56.02bar }$.
Therefore, the total pressure of the mixture is ${ 56.02bar }$.

Additional Information:
Boyle's law: This law states that ‘at a constant temperature, the pressure of a fixed amount (number of moles, n) of a gas is inversely proportional to its volume’.
Charles law: This law states that ‘At constant pressure, the volume of a fixed amount of a gas is directly proportional to its absolute temperature’.
Avogadro’s law: This law states that ‘under the same conditions of temperature and pressure, equal volumes of all gases contain an equal number of molecules’.

Note: The possibility to make a mistake is that you have to calculate the pressure in bar, so use the value of Universal gas constant ${ R=0.083bardm }^{ 3 }{ K }^{ -1 }{ mol }^{ -1 }$, not ${ 8.314JK }^{ -1 }{ mol }$.