Question

What is the volume at STP of 10L of gas initially at 546K and 2 atm?
A.5 L
B.10 L
C.15 L
D.20 L
E.25 L

Answer 1

To solve this question, we must first establish the ideal gas equation must be written for both the initial and final conditions. Then, we must equate these two equations on the basis of the common parameters to find the final answer.

Complete Step-by-Step Answer:
Before we move forward with the solution of the given question, let us first understand some important basic concepts.
Ideal gas law can be understood as combined equational form of the Boyle’s Law, Charles’s Law, Avogadro’s Law and Gay – Lussac’s Law in an empirical form. It establishes a relation between the different physical characteristics of a gas. A gas which obeys the ideal gas law is known as an ideal gas. To put it in simpler terms, it is a mathematical relation between the different physical characteristics of an ideal gas like pressure, volume, no. of moles of the gas and the temperature of the gas. This law can be mathematically be represented as:
$PV = nRT$
In the given question, let us first write the ideal gas equation for both the initial and final conditions.
Initial condition: ${P_1}{V_1} = {n_1}R{T_1}$
Final condition: ${P_2}{V_2} = {n_2}R{T_2}$
Since the number of moles of in both the initial and final conditions are the same, we can say that:
${n_1} = {n_2}$
$\Rightarrow$ $\dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}}$
The values of temperature and pressure at STP are 1273 K and 1 atm respectively.
$\Rightarrow$ ${V_1} = \dfrac{{{P_2}{V_2}}}{{{T_2}}} \times \dfrac{{{T_1}}}{{{P_1}}}$
$\Rightarrow$ ${V_1} = 10L$

Hence, Option B is the correct option

Note: An alternative form of the ideal gas can be given as the chemical amount (n) (in moles) is equal to total mass of the gas (m) (in kilograms) divided by the molar mass (M) (in kilograms per mole)