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Chapter 9: Problem 1237

The volume of a gas at pressure \(21 \times 10^{4} \mathrm{Nm}^{-2}\) and temperature \(27^{\circ} \mathrm{C}\) is 83 Liters. If $\mathrm{R}=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$. Then the quantity of gas in \(\mathrm{g}\) -mole will be (A) 42 (B) 7 (C) 14 (D) 15

Short Answer

Expert verified
The quantity of gas in gram-moles is \(7\). (B)

Step by step solution

01

Convert the volume from Liters to cubic meters

Given the volume of the gas is given in liters, but we need it in cubic meters to work with the units given for pressure and R. Conversion: 1 Liter = 0.001 cubic meters. So, V = 83 Liters × 0.001 = 0.083 m³
02

Convert the temperature from Celsius to Kelvin

We also need to convert the temperature from Celsius to Kelvin. T(K) = T(°C) + 273.15 T(K) = 27°C + 273.15 = 300.15 K
03

Use the Ideal Gas Law to Determine the Number of Moles

Now, we have all the values we need to plug into the ideal gas equation: PV = nRT. P = 21 × 10⁴ Nm² V = 0.083 m³ R = 8.3 J mol⁻¹ K⁻¹ T = 300.15 K Let's now solve for 'n', the number of moles: n = PV / RT
04

Calculate the Number of Moles

Plugging in the values, we get n = (21 × 10⁴ × 0.083) / (8.3 × 300.15) After performing the calculations, we find that n ≈ 7
05

Select the Correct Answer

From the given options, the correct answer is (B) 7 So, the quantity of gas in gram-moles is 7.

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Most popular questions from this chapter

For a gas if ratio of specific heats at constant pressure and volume is \(\gamma\), then value of degrees of freedom is (A) \([2 /(\gamma-1)]\) (B) \([(25) / 2](\gamma-1)\) (C) \([(3 \gamma-1) /(2 \gamma-1)]\) (D) \((9 / 2)(\gamma-1)\)

The root mean square speed of hydrogen molecules of an ideal hydrogen kept in a gas chamber at \(0^{\circ} \mathrm{C}\) is \(3180 \mathrm{~ms}^{-1}\). The pressure on the hydrogen gas is (Density of hydrogen gas is $8.99 \times 10^{-2} \mathrm{~kg} / \mathrm{m}^{3}, 1 \mathrm{~atm}=1.01 \times 10^{5} \mathrm{Nm}^{-2}$ ) (A) \(1.0 \mathrm{~atm}\) (B) \(3.0 \mathrm{~atm}\) (C) \(2.0 \mathrm{~atm}\) (D) \(1.5 \mathrm{~atm}\)

A cylinder contains \(10 \mathrm{~kg}\) of gas at pressure of $10^{\prime} \mathrm{N} / \mathrm{m}^{2}$. The quantity of gas taken out of the cylinder, if final pressure is \(2.5 \times 10^{6} \mathrm{Nm}^{-2}\). will be (temperature of gas is constant) (A) \(5.2 \mathrm{~kg}\) (B) \(3.7 \mathrm{~kg}\) (C) \(7.5 \mathrm{~kg}\) (D) \(1 \mathrm{~kg}\)

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Hydrogen gas is filled in a balloon at \(20^{\circ} \mathrm{C}\). If temperature is made \(40^{\circ} \mathrm{C}\), pressure remaining the same what fraction of hydrogen will come out (A) \(0.75\) (B) \(0.07\) (C) \(0.25\) D) \(0.5\)
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