A mixture of hydrogen and oxygen has volume 500 cm3, temperature 300K, pressure 400 kPa and mass 0.76g. The ratio of masses of oxygen to hydrogen will be:-

Using Ideal gas Equation :PV = nRT ⇒ n = P V R T = 4 0 0 × 1 0 3 × 5 0 0 × 1 0 − 6 8 . 3 × 1 0 0 = 0 . 0 0 8 <!- [if gte mso 9]><xml> </xml><! [endif]-> => m 1 = 0 . 1 2 , m 2 = 0 . 6 4 <!- [if gte mso 9]><xml> </xml><! [endif]->=> m 2 m 1 = 1 6 3 <!- [if gte mso 9]><xml> </xml><! [endif]->

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Physics Thermodynamics Physics Class 11th Thermodynamics

A mixture of hydrogen and oxygen has volume 500 cm³, temperature 300K, pressure 400 kPa and mass 0.76g. The ratio of masses of oxygen to hydrogen will be:-

Option 1 -

3 : 16

Option 2 -

16 : 3

Option 3 -

3 : 8

Option 4 -

8 : 3

2 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

2 months ago

Correct Option - 2

Detailed Solution:

Using Ideal gas Equation :

PV = nRT

$\Rightarrow n = \frac{P V}{R T} = \frac{400 \times 1 0^{3} \times 500 \times 1 0^{- 6}}{8.3 \times 100} = 0.008$

=> $m_{1} = 0.12, m_{2} = 0.64$

=> $\frac{m_{2}}{m_{1}} = \frac{16}{3}$

Using Ideal gas Equation :PV = nRT <math> <mrow> <mo>⇒</mo> <mi>n</mi> <mo>=</mo> <mfrac> <mrow> <mi>P</mi> <mi>V</mi> </mrow> <mrow> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>4</mn> <mn>0</mn> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>3</mn> </mrow> </msup> <mo>×</mo> <mn>5</mn> <mn>0</mn> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>6</mn> </mrow> </msup> </mrow> <mrow> <mn>8</mn> <mo>.</mo> <mn>3</mn> <mo>×</mo> <mn>1</mn> <mn>0</mn> <mn>0</mn> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>0</mn> <mn>0</mn> <mn>8</mn> </mrow> </math>   <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1815997424"> </o:OLEObject></xml><! [endif]-> => <math> <mrow> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>1</mn> <mn>2</mn> <mo>, </mo> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>6</mn> <mn>4</mn> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1815997425"> </o:OLEObject></xml><! [endif]->=> <math> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mn>6</mn> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1815997426"> </o:OLEObject></xml><! [endif]->

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A mixture of hydrogen and oxygen has volume 500 cm³, temperature 300K, pressure 400 kPa and mass 0.76g. The ratio of masses of oxygen to hydrogen will be:-

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