At 1000 K, the value of Kc for the reaction C1s2 + H2O1g2 ∆ CO1g2 + H21g2 is 3.0 * 10-2. Calculate the equilibrium concentrations of H2O, CO2, and H2 in a reac- tion mixture obtained by heating 6.00 mol of steam and an excess of solid carbon in a 5.00-L container. What is the molar composition of the equilibrium mixture?

Video transcript

Hi everyone for this problem. It reads for the reaction, the value of the equilibrium constant at 500 kelvin is 2. times 10 to the negative three If four moles of chlorine and an excess of solid carbon are introduced to a two liter vessel, determine the concentrations of chlorine and carbon tetrachloride. When the reaction mixture reaches equilibrium, calculate the molar composition of the equilibrium mixture. Okay, so the question that we want to answer for this problem is we want to determine the concentrations of chlorine and carbon tetrachloride when the mixtures reach equilibrium. Okay, so we're going to need to construct an ice table to do this. And let's start off by writing out our reaction. So we have our carbon plus our chlorine and we have carbon touch or chloride. Okay, for our ice table, we're going to write out ice and plug in our initial concentrations for the first row of the table. Okay, So for the first row of our table we need to figure out the initial concentration of chlorine. Okay. And the problem, we're told that there is formals of corinne. Okay. And recall, we're looking for the concentration. Okay. And concentration is moles over leader. So we know how many moles we have. We have four moles. And and the problem, we're told that the volume of the vessel is two leaders. Okay, so we're gonna take our moles and divided by two leaders and we're going to get to moller as our concentration for chlorine. So this is the value we're going to put here, Okay, I put it under the wrong thing. So it should be under here. And for an ice table we're going to ignore the carbon because it's a solid. We only include um We exclude solids and liquids in the equilibrium expression and ice table. So let's just go ahead and remove it completely. All right. So then what we're going to get for our reaction then is the following. Alright, and we have zero products. So that means our reaction is going to move in the four direction. So our concentration of reactant is going to decrease in, our concentration of products is going to increase. So for our change for reactant we're going to have a minus and we have two moles of our reactant. So this is going to become -2 x. And then for our product we're gaining products. So the sign is positive and it's just one mole of it. So it's just plus X. All right? So, when we combine the I. And the hero of our ice table, that gives us the zero. So we get two minus two X. And then we get X. Okay, so let's go ahead and just move this over to the side. This is what we use to solve for the initial concentration of chlorine. Now we're going to write out our equilibrium expression, Okay, so that is K. C. Is going to equal the concentration of products over the concentration of react mints. And when we look at our reaction, our concentration of carbon tetrachloride over the concentration of chlorine and we have two moles of it. So that to now becomes an exponent. Okay, so like I said, carbon is not included in the equilibrium expression since it's a solid. Now we know what the value is for our equilibrium constant. And the problem we're told the value is 2.5 times 10 to the negative three. So let's go ahead and simplify this. Bye. Before we simplify let's go ahead and write out what's in the equilibrium row of our ice table for our concentration of product. It is X. And on the equilibrium row our concentration of reactant is to minus two. X. Okay, so now all we really care about is K. C equals the following. Alright, so we know what our equilibrium expression. K equilibrium constant. K C. Is. It was given in the problem and that value is 2. times 10 to the negative three is going to equal x over 2.00 - X. Alright, so based off of our ice table, we will be able to solve for the equilibrium for them for both the chlorine and carbon tetrachloride by solving for X. Okay, so our goal here is to solve for X. And this should have a square here. I didn't bring the square down. Should be a square there as well. Okay, so let's go ahead and move forward. So we're going to determine the value for dividing the initial concentration by the equilibrium constant. If this value is greater than 500, we don't need to use the quadratic formula to solve for X, but if it's less than 500 we do need to use it. We do need to use the quadratic equation. Okay, so we're gonna take the concentration of course this is the initial concentration of chlorine and we're going to divide it by the equilibrium constant. Okay, so we're going to get to Divided by our equilibrium constant is 2.5 times 10 to the -3. And this gives us 800. Okay. And so since 800 is greater than 500, there is no need to use the quadratic formula. Okay, so the two x and the denominator on the right side of the equation can be neglected. Alright, so what this now becomes then in terms of our new equation Or a simplified equation is 2.50 times to the -3 is equal to X over two squared. So we got rid of the minus two X. Because it's negligible. Alright, so now what we want to do is solve for X. Okay, and when we solve for X, what we're going to get is X is equal to one times 10 to the negative to moller. And based off our ice table this represents the concentration of carbon tetrachloride at equilibrium. Okay, so that means now we can solve for the concentration of chlorine at equilibrium at equilibrium. Based off our ice table it's equal to two minus two times X. And we know what X. Is. So let's plug in X. Here. So now we know what our molar concentrations are for chlorine and for our carbon tetrachloride. So to determine so let's go ahead and write that and highlight them as our final answer. So for then that's for the first part. So our concentration molar concentration for carbon tetrachloride is equal to one times 10 to the negative two. And our concentration for chlorine gas is equal to 1.98 moller. So we can highlight that as the first part of our answer. Okay. And the second part is to determine the molar composition of the mixture. So let's go back up. So we determine the concentrations of chlorine and carbon tetrachloride. Now we need to calculate the molar composition of the equilibrium mixture. So let's go ahead and do that. So to determine the molar composition of the equilibrium mixture, we're going to calculate the number of moles of each component at equilibrium. Okay, so the number of moles is represented by n. So we're going to calculate the number of moles of carbon tetrachloride. Okay, so we're going to take the concentration of carbon tetrachloride at equilibrium and we're going to multiply it by the volume of solution. Okay, so we're going to get one Times 10 to the negative to moller Times two leaders gives to Times 10 to the -2 moles of carbon tetrachloride or of Yes, carbon tetrachloride. Okay. And for the number of moles for corinne, this is equal to the concentration of chlorine at equilibrium times the volume. So we have 1.98 moller Times two leaders gives 3. malls of chlorine. Okay, so now we can calculate the total number of moles. We're going to calculate the total number of moles by adding these two together. So we get the number of moles of carbon tetrachloride plus the number of moles of chlorine. So we get two Times 10 to the -2 moles plus 3.96 moles gives 3.98 moles. And now we can calculate the molar composition of each component. So let's do this in a different color. The molar composition of carbon tetrachloride is going to equal the number of moles of carbon tetrachloride over the total number of moles. So we have two times 10 to the negative two moles over 3.98 moles gives 0.005. So our molar composition of carbon tetrachloride is equal to 0.005. So we can go ahead and highlight that. And lastly we're going to calculate the Moeller composition of corning and it's going to equal the number the is going to equal the number of moles of that component over the total moles. So we have 3. moles over 3.98 moles And this equals zero 995. So in terms of let's just make a little bit of space here. So for our Mueller composition of chlorine, It is equal to 0.995 and that's going to be our final answer. That is all parts of this question answered. That's the end of this problem. I hope this was helpful.