Question

$1 \,mole$ of $H_2$ gas is contained in a box of volume $V\, = \,1.00 \,m^3$ at $T\, =\, 300 \,K$. The gas is heated to a temperature of $T\, =\, 3000\, K$ and the gas gets converted to a gas of hydrogen atoms. The final pressure would be (considering all gases to be ideal)

• A. same as the pressure initially
• B. 2 times the pressure initially
• C. 10 times the pressure initially
• D. 20 times the pressure initially

Answer 1

Answer: (D)

According to gas equation
$\quad\quad$$\quad\quad$$\quad\quad$$\quad\quad$$\quad\quad$$\quad\quad$PV = nRT
or $\frac{P_{2}V_{2}}{T_{2}}=\frac{P_{1}V_{1}}{T_{1}}or \frac{P_{2}}{P_{1}}=\frac{V_{1}}{V_{2}}. \frac{T_{2}}{T_{1}}$
Here, T₂ = 3000 K, T₁ = 300 K
Since H₂ splits into hydrogen atoms, therefore
volume become half i.e., $V_{2}=\frac{1}{2}V_{1}$
$\therefore \frac{P_{2}\quad}{P_{1}}=\frac{V_{1}}{\frac{1}{2}V_{1}}\times\frac{3000}{300}$
or$\quad \frac{P_{2}}{P_{1}}=20$