Hydrogen gas (a potential future fuel) can be formed by the reaction of methane with water according to the equation: CH4( g) + H2O( g)¡CO( g) + 3 H2( g) In a particular reaction, 25.5 L of methane gas (measured at a pressure of 732 torr and a temperature of 25 °C) mixes with 22.8 L of water vapor (measured at a pressure of 702 torr and a temperature of 125 °C). The reaction produces 26.2 L of hydrogen gas at STP. What is the percent yield of the reaction?

Video transcript

Welcome back everyone to another video, hydrogen gas, a potential future fuel can be formed by the reaction of methane with water. According to the equation, CH four plus h2o produces co and three modes of H two in a particular reaction. 25.5 L of methane gas measured at a pressure of 732 tor and a temperature of 25 °C mixes with 22.8 L of water vapor measured at a pressure of 702 tor and a temperature of 125 °C. The reaction produces 26.2 L of hydrogen gas at standard temperature and pressure. What is the percent yield of the reaction? And we're given for answer choices. A 84.3%. B 23.4% C 60.4% and D 52.1%. Now, this is an ideal gas law problem. We are going to use an equation PV equals N RT. And because we're given our balanced equation, it would be sensible to find the number of moles for each substance using PV and dividing it by RT So this is how we rearrange our equation. And now let's identify the number of moles of each reactant to begin with. Starting with methane. We want to use pressure that would be 732 tour or toward Ching. We want to use atmospheres and studs. So let's use a conversion factor which tells us that one atmosphere is equivalent to 1 to 760 to, we're going to use volume per V. So now we have 25.5 L on the bottom of our fraction. Let's use R that's the universal gas constant, 0.08206 liters multiplied by atmospheres divided by a mole multiplied by Kelvin. And now we need temperature that's 25 °C. But let's not forget to convert that into Kelvin. So we're adding 273.15. Now, the result that we get is a 1.004 moles, that's the amount of methane. And now we want to calculate the number of moles of water vapor. So we are going to do that using the same approach. What is our pressure? 702 tour, let's use our conversion factor. One atmosphere is equivalent to 760 to R. Let's use volume 22.8 L. Now let's include our universal gas constant 0.08206. Now, temperature 125 °C. We are converting that into Kelvin. Let's see what we get. That will be zero point 645 moles. Now, we can actually identify the limiting reactant because the reaction is 1 to 1 ratio, the lower number represents the limiting reactant. So we can say that water vapor is the limiting reactant. But now let's go ahead and calculate the number of moles of hydrogen right now to calculate the number of moles of hydrogen, we can use either the same law or we can make it faster. We can say that the number of moles of hydrogen that would not be the theoretical yield. That would be the actual yield. If we know that we have 26.2 L produced at STP, we can divide that volume by the volume in one mole of any gas at STP, which is 22.4. So this is the molar volume at STP. And if we find the ratio, we get 1.169 moles of hygiene produced. Now, let's find the theoretically yield of hydrogen. Let's remember that the limiting reactant in this case is water. So first of all, the number of moles of hygiene expected to form theoretically would be three times greater because we have a 1 to 3 ratio between water and hydrogen. So we're going to say that this would be three multiplied by the number of moles of water vapor. So three multiplied by 0.645 moles once again, how do we know that? Well, essentially the reaction tells us that one mole of water vapor produces three moles of hydrogen. So we need to modify that result by three, essentially, we can calculate the result and we end up with one point nine, we were most. So we want to understand that this is the theoretical yield. This is the actual yield previously calculated. So the percent yield would be the ratio between the actual amount we can use 1.169 moles and the theoretical amount. So that would be 1.934 moles. We're going to convert that expression into the percentage multiplying by 100%. And we noticed that we get a result of 60.4%. So now what do we see in our answer choices? Essentially considering the answer choices, we can easily conclude that the correct answer to this problem is option C 60.4% is the percent yield of the reaction. Thank you for watching. And I hope to see you in the next video.