1 mole of H₂ gas is contained in a box of volume V = 1.00 m³ at T = 300K. The gas is heated to a temperature of T = 3000K 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

This is a multiple choice answer as classified in NCERT Exemplar

(d) When number of molecules breaks then number of moles would become double.

P $\propto nT$ where n is the number of moles and T is temperature of ideal gas

As gases breaks number of moles becomes twcice of initial so n₂ =2n₁

$\frac{P_2}{P_1}=\frac{n_2{T}_2}{n_1{T}_1}=\frac{2n_1\left(3000\right)}{n_1\left(300\right)}$ = 20

p₂=20p₁

so 20 times

<p><span data-teams="true">This is a multiple choice answer as classified in NCERT Exemplar</span></p><p> (d) When number of molecules breaks then number of moles would become double.</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745555406phpOBWcWt_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745555406phpOBWcWt.jpeg" alt="" width="137" height="149"></picture></div></div><p>P <span contenteditable="false"> <math> <mo>∝</mo> <mi>n</mi> <mi>T</mi> </math> </span>where n is the number of moles and T is temperature of ideal gas</p><p>As gases breaks number of moles becomes twcice of initial so n₂ =2n₁</p><p><span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>P</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>P</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>n</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> <msub> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>n</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <msub> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>2</mn> <msub> <mrow> <mrow> <mi>n</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mo> (</mo> <mn>3000</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>n</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mo> (</mo> <mn>300</mn> <mo>)</mo> </mrow> </mrow> </mfrac> </math> </span>= 20</p><p>p₂=20p₁</p><p>so 20 times</p>

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