Class 11th Thermodynamics Physics Physics Thermodynamics

A mixture of hydrogen and oxygen has volume 2000 cm³, temperature 300K, pressure 100 kPa and mass 0.76g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be:

[Take gas constant R = 8.3 JK^-¹ mol^-¹]

Option 1 - <p> <span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> </mrow> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>1</mn> </mrow> </mfrac> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>1</mn> <mn>6</mn> </mrow> </mfrac> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> <mn>6</mn> </mrow> <mrow> <mn>1</mn> </mrow> </mfrac> </mrow> </math> </span></p>

17 Views|Posted 7 months ago

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Answered by

Vishal Baghel | Contributor-Level 10

7 months ago

Correct Option - 2

Detailed Solution:

$V_{T} = 2000 c m^{3} = 2000 * 1 0^{- 6} m^{3} (T o t a l v o l u m e o f m i x t u r e)$

T = 300 K

$_{}^{}^{}$ $P_{T} = 100 k P a = 100 * 1 0^{3} P a = 1 0^{5}$ Pa

mT = 8.3 J/K1 mol1

Now, using Ideal gas equation

$P_{T} V = (x_{1} + x_{2}) R T$

$\Rightarrow 1 0^{5} * 200 * 1 0^{- 6} = (x_{1} + x_{2}) * 8.3 * 300$

$\frac{x_{1}}{x_{2}} = \frac{0.06}{0.02} = 3 : 1$

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