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Calculate the volume occupied by \[8.8\] gram of \[CO_2\] at \[31.1\] degree Celsius and \[1\] bar pressure R= \[0.083\] by LK inverse mole inverse (molecular mass of \[CO_2 = 44\] gram mole inverse)

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Last updated date: 23rd Apr 2024
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Answer
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Hint: According to the ideal gas law, the product of volume and temperature is equal to the number of moles, universal gas constant, and temperature. The moles can be defined as the ratio of mass to molar mass. The mass of \[CO_2\] was already given whereas the molar mass of \[CO_2\] was also given.
Formula used:
\[PV = nRT\]
P is pressure
V is volume
n is number of moles
R is universal gas constant
T is temperature

Complete answer:
The ideal gas law is also known as the general gas equation. It relates the pressure, volume, temperature, number of moles, and universal gas constant.
Moles relate the ratio of the mass and molar mass. The given gas is carbon dioxide. It has a mass of \[8.8\] gram. The mass occupied by one mole of carbon dioxide is \[44\] atomic mass units, which is nothing but molar mass.
By substituting all the given values in the above formula,
\[V = \dfrac{{8.8 \times 0.083 \times 304.1}}{{44 \times 1}}\]
The volume V will be \[5.0486L\]
Thus, the volume occupied by \[8.8\] gram of \[CO_2\] at \[31.1\]degree Celsius and \[1\] bar pressure R= \[0.083\] by LK inverse mole inverse (molecular mass of \[CO_2 = 44\] gram mole inverse) will be \[5.0486L\]

Note:
While calculating any term or quantity related to ideal gas law, the units must be considered. As the pressure must be in atm, and the volume must be in Litres, the temperature must be in kelvins, and the number of moles in moles only.
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