Question

Consider the four gas samples described in the following table, showing the number of mole (n), absolute temperature $\left(T_k\right)$, and volume (V).

Flask No.	n(mol)	T(K)	V(L)
$1$	$2$	$200$	$2$
$2$	$3$	$300$	$2$
$3$	$2$	$400$	$4$
$4$	$3$	$500$	$4$

The ideal gas law is an important equation in chemistry. It can be used to calculate the properties of a gas sample.

Based on the information given in the table above, which two of these four flasks should have the SAME value of gas pressure?

• A. Flasks $1$ and $2$
• B. Flasks $1$ and $3$
• C. Flasks $2$ and $3$
• D. Flasks $3$ and $4$

Answer 1

The correct option is B Flasks $1$ and $3$

$\text{We know, ideal gas equation,}PV=nRT$

$\begin{array}{cc}\text{where,}& P\to \text{Pressure of}gas\\ V& \to \text{volume}\\ n& \to \text{mole of}gas\end{array}$

$\begin{array}{cc}\text{Flask}1\to & n=2\\ T& =200k\\ V& =2L\end{array}{P}_1=\frac{n_{1}R{T}_1}{v_1}=\frac{2,xR\times 200}{2}=200R.$

$\begin{array}{cc}\text{Flask}2\to & n=3\\ T& =300k{P}_2=\frac{n_{2}R{T}_2}{V_2}=\frac{3\times R\times 300}{2}=450R\\ & V=2L\end{array}$

$\begin{array}{cc}\text{Flask}3\to & n=2\\ T& =400k{P}_3=\frac{n_{3}R{T}_3}{V_3}=\frac{2\times R\times 400}{4}=200R\\ & V=4L\end{array}$

$\begin{array}{cc}\text{flask}4\Rightarrow n& =3,P_4=\frac{n_{4}R{T}_4}{V_4}=\frac{3\times R\times 500}{4}=375R\\ T& =500k\\ V& =4L\end{array}$

$\begin{array}{c}\text{Hence, Flasks}1\text{and}3\text{have same value of gas pressure.}\\ \text{so, option (B) is correct.}\end{array}$