Question

If the volume of $2moles$ of an ideal gas at $546K$ is $44.8litres$ then its pressure will be:
A.) $1atm$
B.) $2atm$
C.) $3atm$
D.) $4atm$

Answer 1

This question can be solved by the concept of ideal gas equation according to which for an ideal gas the product of pressure and volume is equal to the product of number of moles, gas constant and temperature.

Complete step by step answer:
As we are given in question that the given gas is an ideal gas and also, we know that the pressure of an ideal gas can be calculated from the ideal gas equation. The ideal gas equation is the equation of state of a hypothetical ideal gas. This is because the ideal gas conditions cannot be obtained and it is not practical to have a pure ideal gas . This ideal gas equation is also called the general gas equation. According to the ideal gas equation, the product of pressure ($P$) and volume ($V$) is equal to the product of number of moles ($n$), gas constant ($R$) and temperature ($T$). The ideal gas equation can be simply expressed as:
$PV = nRT$ or
$P = \dfrac{{nRT}}{V}$ $- (1)$
Where, $P =$ Pressure of the gas
$V =$ Volume of the gas
$n =$ number of moles
$R =$ ideal gas constant $= 0.082LatmMo{l^{ - 1}}{K^{ - 1}}$
$T =$ Temperature
As we are given in question that Volume($V$) of gas is $44.8litres$, Temperature ($T$) is given as$546K$ and number of moles ($n$) of the gas is $2moles$. Now, by putting all given values in equation $- (1)$ we get:
$P = \dfrac{{2 \times 0.082 \times 546}}{{44.8}} \\\ \Rightarrow P = 2atm \\\$

Hence, option B is the correct answer.

Note: Remember that the ideal gas equation can be obtained by combining all the simple laws. These laws are Boyle’s law, Charles law and Avogadro law. According to Boyle law pressure is inversely proportional to volume at a given temperature that is $P\propto \dfrac{1}{V}$. According to Charles law, volume is directly proportional to temperature at given pressure that is $V\propto T$ and according to Avogadro law, volume is directly proportional to number of moles at constant pressure and temperature that is $(V\propto {\text{ }}n)$. Therefore, by combining these laws we get the ideal gas law ($PV = nRT$).