Aluminum (Al) and iron (Fe) each react with hydrochloric...

Aluminum (Al) and iron (Fe) each react with hydrochloric acid solution (HCl) to produce a chloride salt and hydrogen gas, $\mathrm{H}_{2}(\mathrm{g}) .$ A $0.1924 \mathrm{g}$ sample of a mixture of $\mathrm{Al}$ and $\mathrm{Fe}$ is treated with excess HCl solution. A volume of $159 \mathrm{mL}$ of $\mathrm{H}_{2}$ gas is collected over water at $19.0^{\circ} \mathrm{C}$ and 841 Torr. What is the percent (by mass) of Fe in the mixture? The vapor pressure of water at $19.0^{\circ} \mathrm{C}$ is 16.5 Torr.

Key Concepts

Stoichiometry of Acid?Metal Reactions

This concept involves understanding and applying the balanced chemical equations for reactions between metals and hydrochloric acid, where metals react to form their corresponding chloride salts and hydrogen gas. It is crucial for determining the molar relationships between the reactants and products, which, in turn, allows one to relate the amount of hydrogen gas produced to the amounts of metals present in the mixture.

Ideal Gas Law

The ideal gas law is a fundamental equation (PV=nRT) used to relate the pressure, volume, temperature, and number of moles of a gas. In problems involving gas collection, it enables the conversion of measured gas volumes and adjusted pressures into moles of gas, linking macroscopic observations with molecular quantity scales.

Adjustment for Water Vapor Pressure

When gases are collected over water, the measured total pressure includes both the gas and the water vapor. To accurately determine the partial pressure of the reacting gas, it is necessary to subtract the vapor pressure of water from the total pressure. This correction is essential to ensure that the calculations based on the ideal gas law yield correct molar amounts.

Percent Composition Calculation

This concept involves determining the mass percentage of each component in a mixture. By relating the calculated moles of reacting substances (derived through stoichiometry and gas law calculations) back to their respective masses and comparing these to the total mass of the mixture, one can determine the percent by mass of a specific component, such as iron in this context.

Transcript

00:17 In this question we're given that we have a mixture of aluminum and iron and that they each react with hydrochloric acid to produce a chloride salt and hydrogen gas.

00:26 We're asked what the percent by mass of iron in this mixture is given that we have 159 millimeters of hydrogen gas collected over water at 19 degrees celsius and 841 tours.

00:40 So the first thing we want to do with this question is recognize that this is a mixture.

00:44 And for a mixture, we're going to want to write two separate equations.

00:49 So we're given that aluminum and iron, each react with hydrochloric acid, to form a chloride salt, as well as hydrogen gas.

01:21 So we also need to make sure that these equations are balanced.

01:28 So let's go ahead and do that as well.

01:38 We need to put three in front of here and so we have two in front of here or i'm sorry okay so now that we have that we need to actually set up a system of equations for this to work so we know that this mixture has a mass of 0 .1924 grams so what we're actually going to do is we're going to put x plus y equals this now x we're going to have as the mass of iron and y is going to be the mass of aluminum.

03:13 Now we're also given the amount of hydrogen gas that is produced from this reaction.

03:21 So we know that at 19 degrees celsius we collected 159 milliliters of hydrogen gas with the pressure of 841 towards.

03:37 Now because this pressure was collected over water, we need to subtract the vapor pressure from it, which is 16 .5 tours.

03:49 So our actual pressure of hydrogen is going to be 824 .5 tours.

03:58 Now we can find the moles of hydrogen produced by using the ideal gas law.

04:05 And we're going to rearrange this really quickly.

04:07 Set it equal to moles.

04:11 Now we have all the information we need here.

04:13 We know we have 0 .159 liters.

04:17 We are at 19 degrees celsius, which is equal to 292 kelvin.

04:25 Our pressure is 824 .5 tours, which is equal to, if you divide this by 160, or i'm sorry, 760, 1 .08 atmospheres.

04:41 And r is just our gas constant.

04:45 So let's go ahead and plug all this in.

04:57 Get n equals 0 .0072 moles.

05:05 Now this is the total amount of hydrogen produced from this mixture.

05:10 So we're going to need another equation to calculate this amount...

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