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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

A balloon filled with helium has a volume of \(1.28 \times 10^{3} \mathrm{~L}\) at sea level where the pressure is \(0.998\) atm and the temperature is \(31^{\circ} \mathrm{C}\). The balloon is taken to the top of a mountain where the pressure is \(0.753 \mathrm{~atm}\) and the temperature is \(-25^{\circ} \mathrm{C}\). What is the volume of the balloon at the top of the mountain?

Tank A has ammonis at \(300 \mathrm{~K}\), Tank B hes nitrogen gas at \(150 \mathrm{~K}\). Thaks A and B have the same volume. Compare the presrures in tanks \(A\) and \(B\) if (a) tank B has twice as many moles of nitrogen as tank \(A\) has of ammonia. (b) tank A has the same number of moles of ammonia as tank \(\mathrm{B}\) has of nitrogen. (Try to do this without a calculatorl)

A 2.00-L tank, evacuated and empty, has a mass of \(725.6 \mathrm{~g}\). It is filled with butane gas \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)\) at \(22^{\circ} \mathrm{C}\) to a pressure of \(1.78 \mathrm{~atm} .\) What is the mass of the tank after it is filled?

A \(0.2500-\mathrm{g}\) sample of an \(\mathrm{Al}-\mathrm{Zn}\) alloy reacts with \(\mathrm{HCl}\) to form hydro- gen gas: $$ \begin{aligned} &\mathrm{Al}(s)+3 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Al}^{3+}(a q)+\frac{3}{2} \mathrm{H}_{2}(g) \\ &\mathrm{Zn}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+\mathrm{H}_{2}(g) \end{aligned} $$ The hydrogen produced has a volume of \(0.147 \mathrm{~L}\) at \(25^{\circ} \mathrm{C}\) and \(755 \mathrm{~mm} \mathrm{Hg}\) What is the percentage of zinc in the alloy?

Nitrogen can react with steam to form ammonia and nitrogen oxide gases. A 20.0-L sample of nitrogen at \(173^{\circ} \mathrm{C}\) and \(772 \mathrm{~mm} \mathrm{Hg}\) is made to react with an excess of steam. The products are collected at room temperature \(\left(25^{\circ} \mathrm{C}\right)\) into an evacuated flask with a volume of \(15.0 \mathrm{~L}\). (a) Write a balanced equation for the reaction. (b) What is the total pressure of the products in the collecting flask after the reaction is complete? (c) What is the partial pressure of each of the products in the flask?
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