Hydrogen gas (a potential future fuel) can be formed by the...

Hydrogen gas (a potential future fuel) can be formed by the reaction of methane with water according to the equation: $$\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+3 \mathrm{H}_{2}(g)$$ In a particular reaction, 25.5 $\mathrm{L}$ of methane gas (at a pressure of 732 torr and a temperature of $25^{\circ} \mathrm{C} )$ mixes with 22.8 $\mathrm{L}$ of water vapor $(\mathrm{at}$ a pressure of 702 torr and a temperature of $125^{\circ} \mathrm{C} )$ . The reaction produces 26.2 $\mathrm{L}$ of hydrogen gas at STP. What is the percent yield of the reaction?

Hydrogen gas (a potential future fuel) can be formed by the reaction
of methane with water according to the equation:
$$\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+3 \mathrm{H}_{2}(g)$$
In a particular reaction, 25.5 $\mathrm{L}$ of methane gas (at a pressure of 732
torr and a temperature of $25^{\circ} \mathrm{C} )$ mixes with 22.8 $\mathrm{L}$ of water vapor $(\mathrm{at}$ a pressure of 702 torr and a temperature of $125^{\circ} \mathrm{C} )$ . The reaction produces 26.2 $\mathrm{L}$ of hydrogen gas at STP. What is the percent yield of the reaction?

Key Concepts

Standard Temperature and Pressure (STP)

STP refers to the standard conditions for temperature and pressure, typically defined as 0°C (273.15 K) and 1 atm pressure. It provides a common reference point that simplifies calculations and comparisons of gas volumes in reactions.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure, volume, temperature, and number of moles of a gas. This fundamental concept allows the conversion between volume and moles under various conditions, which is necessary when dealing with gases that are not measured under the same conditions.

Percent Yield

Percent yield is a measure of the efficiency of a reaction, calculated by comparing the actual yield (the amount of product obtained experimentally) to the theoretical yield (the amount predicted by stoichiometry). It quantifies the effectiveness of the reaction and helps identify any losses during the process.

Chemical Reaction Stoichiometry

This concept involves using the balanced chemical equation to determine the mole ratio of reactants and products in a chemical reaction. It is essential for calculating how much product can be theoretically formed from given amounts of reactants, and hence is a foundation for predicting reaction outcomes.

Limiting Reactant

The limiting reactant is the substance that is completely consumed first, thus determining the maximum amount of product that can be formed in a chemical reaction. Identifying the limiting reactant is vital when reactants are not present in the exact stoichiometric amounts required by the balanced equation.

Transcript

00:01 All right, so in this question, we are giving this potential reaction to produce hydrogen gas, and we're asked to calculate the percent yield of this reaction.

00:10 So the first thing we need to do is first calculate which one of these, whether it's methane or water vapor, it's going to be the limiting reagent.

00:18 How we do that is we're going to calculate the number of moles each.

00:22 Notice that these both have a one -to -one molar ratio.

00:26 So whichever one has less moles should just be the limiting reactant.

00:31 All right, so to start, we're going to calculate the moles of methane.

00:38 So we're going to have n of ch4 as equal to, we know for this whole problem, that n is equal to pv over rt.

00:50 So with that being said, we can calculate the number of moles of methane.

00:55 Using the pressure it gives us, which is 700 or 732 tours, times the volume, which it gives us is 25 .5 liters over and then rt.

01:08 R is going to be 62 .36, and the units for that is going to be tor times liter over moles times kelvin.

01:20 And then lastly, it gives us a temperature of 25 degrees celsius, which should be equivalent to 298 kelvin.

01:33 So if we run that calculation, you're going to find that we're going to get 1 .00 moles.

01:42 All right.

01:43 So now we get to do the moles of water vapor.

01:46 We're essentially going to go through the exact same process.

01:50 We can find that the moles of h2o equal to the pressure gives us, which is 702, tor, the volume, which is 22 .8 liters over.

02:07 We're going to use the exact same r value.

02:20 And this time it gives us a temperature of 398 degrees kelvin.

02:29 All right, so with all that being said, if you run this calculation, you'll find that the moles of water is 0 .64.

02:37 So with that being said, water is going to be the limiting reagent of this reaction.

02:42 So now we're going to calculate our theoretical yield.

02:46 So i'm just going to write theory here...

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