A mixture of hydrogen and oxygen has volume 2000 \(cm^3\), temperature 300 K, pressure 100 kPa and mass 0.76 g. 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 \(JK^{–1}\) \(mol^{–1}\)]
- \(\frac{1}{3}\)
- \(\frac{3}{1}\)
- \(\frac{1}{16}\)
- \(\frac{16}{1}\)
The Correct Option is B
Solution and Explanation
\(P_1V = n_1RT\)
\(P_2V = n_2RT\)
\(⇒ (100 kPa) V = (n_1 + n_2)RT\)
\(⇒n_1+n_2=\frac{(100 kPa)(2000 cm)^3)}{8.3×300}….(1)\)
Also, \(n_1 × 2 + n_2 × 32 = 0.76 ….(2)\)
Solving (1) and (2),
\(n_1 = 0.06\)
\(n_2 = 0.02\)
\(⇒ \frac{n_1}{n_2} = 3\)
Hence, the correct option is (B): \(\frac{3}{1}\)
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Concepts Used:
Gas Laws
The gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases.
The five gas laws are:
- Boyle’s Law, which provides a relationship between the pressure and the volume of a gas.
- Charles’s Law, which provides a relationship between the volume occupied by a gas and the absolute temperature.
- Gay-Lussac’s Law, which provides a relationship between the pressure exerted by a gas on the walls of its container and the absolute temperature associated with the gas.
- Avogadro’s Law, which provides a relationship between the volume occupied by a gas and the amount of gaseous substance.
- The Combined Gas Law (or the Ideal Gas Law), which can be obtained by combining the four laws listed above.