May be solved by the molar volume method (Section 14.7 ) or...

May be solved by the molar volume method (Section 14.7 ) or by the ideal gas equation method (Section 14.8 ). In the answer section, the setups are given first for the molar volume method, printed over a tan background. Then, over a green back- ground, the answers are given for the ideal gas equation method. Check your work according to the section you studied. How many grams of water must decompose by electrolysis to produce $23.9 \mathrm{L} \mathrm{H}_{2}$, measured at $28^{\circ} \mathrm{C}$ and 728 torr?

May be solved by the molar volume method (Section 14.7 ) or by the ideal gas equation method (Section 14.8 ). In the answer section, the setups are given first for the molar volume method, printed over a tan background. Then, over a green back-
ground, the answers are given for the ideal gas equation method. Check your work according to the section you studied.
How many grams of water must decompose by electrolysis to produce $23.9 \mathrm{L} \mathrm{H}_{2}$, measured at $28^{\circ} \mathrm{C}$ and 728 torr?

Key Concepts

Unit Conversions

Precise calculations in physical chemistry require the consistent use of units for temperature, pressure, and volume. Converting temperatures from Celsius to Kelvin, and pressures from torr or other units to the appropriate unit (such as atm or Pa) ensures that the variables in equations like the ideal gas law are coherent, leading to accurate results.

Molar Volume Concept

Molar volume refers to the volume occupied by one mole of a gas at a specified set of conditions, often under standard temperature and pressure (STP) or other defined conditions. This concept is useful for converting between the measured volume of a gas and the number of moles, thereby facilitating stoichiometric calculations in gas-related reactions.

Ideal Gas Law

The ideal gas law is a fundamental equation (PV = nRT) that relates the pressure, volume, temperature, and number of moles of an ideal gas. This relationship is essential for converting between volume and moles of a gaseous substance under specified conditions, providing a method to calculate the amount of substance when the gas is measured at non-standard temperature and pressure conditions.

Reaction Stoichiometry

This concept involves using the balanced chemical equation for a reaction to relate the moles of reactants to the moles of products. In the context of water electrolysis, the decomposition reaction (typically represented as 2H2O ? 2H2 + O2) allows one to determine how many moles of water decompose to produce a given number of moles of hydrogen gas, making it a vital tool in quantitative chemical analysis.

Transcript

00:02 Right.

00:02 In this problem, we need to start out by writing our balanced equation.

00:07 They tell us that water is being broken down into hydrogen and oxygen.

00:15 So writing my balanced equation gives me 2h2o, breaks into 2h2 plus o2.

00:26 I want to know how many grams of water are needed to produce 23 .9 liters of hydrogen.

00:40 And it's at 28 degrees celsius and 728 tor.

00:50 I'm going to go ahead right away and convert my temperature to kelvin by adding 273, and that gives me 301 kelvin.

01:03 To solve this problem, i'm going to need to do stochialometry.

01:07 However, before i can do that, i need to know how many moles of hydrogen i have.

01:12 I cannot simply use 22 .4 in this problem because i am not.

01:18 At standard temperature and pressure.

01:20 To determine how many moles i have, i'm going to use the ideal gas equation, and i have rearranged it to solve four number of moles.

01:28 So that's going to be pv over rt.

01:34 So let's go ahead and plug in these values to figure out how many moles of hydrogen i have.

01:41 The pressure is 728 or.

01:49 The volume that is given in the problem is 23 .9 liters.

01:59 The r that i'm going to select is the universal gas constant that has tor as one of the units...

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