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Chapter 5: Problem 55

What is the ratio of the rate of effusion of the most abundant gas, nitrogen, to the lightest gas, hydrogen?

Short Answer

Expert verified
Answer: The ratio of the rate of effusion of nitrogen to hydrogen is approximately 1:3.74.

Step by step solution

01

Understanding Graham's Law of Effusion

Graham's law of effusion states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, it can be written as: Rate_1 / Rate_2 = sqrt(Molar_mass_2 / Molar_mass_1) Where Rate_1 and Rate_2 are the rates of effusion of two different gases, and Molar_mass_1 and Molar_mass_2 are their respective molar masses. We will use this formula to calculate the ratio of the rate of effusion of nitrogen (N_2) to hydrogen (H_2).
02

Find the molar masses of nitrogen and hydrogen

First, we need to find the molar masses of nitrogen and hydrogen. The molar mass of a molecule can be found by adding up the atomic masses of all the atoms present in the molecule. For nitrogen (N_2), it consists of 2 nitrogen atoms, and each nitrogen atom has a molar mass of 14.01 g/mol. The molar mass of a nitrogen molecule is: Molar_mass_N2 = 2 * 14.01 g/mol = 28.02 g/mol For a hydrogen molecule (H_2), it consists of two hydrogen atoms, and each hydrogen atom has a molar mass of approximately 1 g/mol. So, the molar mass of a hydrogen molecule is: Molar_mass_H2 = 2 * 1 g/mol = 2 g/mol
03

Apply Graham's Law to find the rate of effusion ratio

Now, we can use Graham's Law to calculate the ratio of the rate of effusion of nitrogen (N_2) to hydrogen (H_2): Rate_N2 / Rate_H2 = sqrt(Molar_mass_H2 / Molar_mass_N2) Plugging in the values that we calculated earlier, we get: Rate_N2 / Rate_H2 = sqrt(2 g/mol / 28.02 g/mol)
04

Simplify the fraction and calculate the ratio

Now, we will simplify the fraction within the square root: Rate_N2 / Rate_H2 = sqrt(1 / 14.01) To find the ratio, calculate the square root: Rate_N2 / Rate_H2 ≈ sqrt(1/14.01) ≈ \dfrac{1}{3.74} So, the ratio of the rate of effusion of nitrogen to hydrogen is approximately 1:3.74, or in other words, hydrogen effuses approximately 3.74 times faster than nitrogen.

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Most popular questions from this chapter

Sketch a cylinder with ten molecules of helium (He) gas. 'The cylinder has a movable piston. Label this aketch before. Make an after abetch to represent (a) decrease in temperature at constant pressure. (b) a decrease in pressure fram \(1000 \mathrm{~mm} \mathrm{Hg}\) to \(500 \mathrm{~mm} \mathrm{Hg}\) at constant temperature. (c) five molecules of \(\mathrm{H}_{2}\) gas added at constant temperature and pressure.

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A mixture in which the mole ratio of hydrogen to oxygen is \(2: 1\) is used to prepare water by the reaction $$ 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) $$ The total pressure in the container is \(0.950 \mathrm{~atm}\) at \(25^{\circ} \mathrm{C}\) before the reaction. What is the final pressure in the container at \(125^{\circ} \mathrm{C}\) after the reaction, assuming an \(88.0 \%\) yield and no volume change?

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