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About 75 percent of hydrogen for industrial use is produced by the steam-reforming process. This process is carried out in two stages called primary and secondary reforming. In the primary stage, a mixture of steam and methane at about 30 atm is heated over a nickel catalyst at $800^{\circ} \mathrm{C}$ to give hydrogen and carbon monoxide:$$\begin{aligned}\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+& 3 \mathrm{H}_{2}(g) \\\Delta H^{\circ} &=260 \mathrm{kJ} / \mathrm{mol}\end{aligned}$$The secondary stage is carried out at about $1000^{\circ} \mathrm{C}$ in the presence of air, to convert the remaining methane to hydrogen:$$\begin{aligned}\mathrm{CH}_{4}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{CO}(g) &+2 \mathrm{H}_{2}(g) \\\Delta H^{\circ} &=35.7 \mathrm{kJ} / \mathrm{mol}\end{aligned}$$(a) What conditions of temperature and pressure would favor the formation of products in both the primary and secondary stage? (b) The equilibrium constant $K_{\mathrm{c}}$ for the primary stage is 18 at $800^{\circ} \mathrm{C}$.(i) Calculate $K_{P}$ for the reaction. (ii) If the partial pressures of methane and steam were both 15 atm at the start, what are the pressures of all the gases at equilibrium?

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(a) high temperature, low pressure(b) $K_{p}=1.4 \times 10^{5}$$P_{\mathrm{CH}_{4}}=1 \mathrm{atm}$$P_{\mathrm{H}_{2} \mathrm{O}}=1$ atm$P_{\mathrm{CO}}=14$ atm$P_{\mathrm{H}_{2}}=42$ atm

Chemistry 102

Chapter 14

Chemical Equilibrium

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10:03

In thermodynamics, a state of thermodynamic equilibrium is a state in which a system is in thermal equilibrium with its surroundings. A system in thermodynamic equilibrium is in thermal equilibrium, mechanical equilibrium, electrical equilibrium, and chemical equilibrium. A system is in equilibrium when it is in thermal equilibrium with its surroundings.

00:54

In chemistry, chemical equilibrium (also known as dynamic equilibrium) is a state of chemical stability in which the concentrations of the chemical substances do not change in the course of time due to their reaction with each other in a closed system. Chemical equilibrium is an example of dynamic equilibrium, a thermodynamic concept.

04:18

About 75 percent of hydrog…

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02:06

The first step in the indu…

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here we have two chemical reactions that are used in the production of hydrogen from steam and methane. In the primary stage, we have methane reacting with steam at 800 degrees Celsius to produce carbon monoxide and hydrogen. And it is Endo thermic secondary stage. It's methane reacting with oxygen to produce carbon monoxide and hydrogen gas, and it's also Endo thermic. So the first question then asks What conditions of temperature and pressure would favor the formation of products for both the primary and the secondary reactions? Well, because they're both endo thermic, then high temperatures will favor the production of product and because both of them have more moles, gas as product than gas as reactant. We've got formals here and to and then we've got three moles in 1.5. So there are more moles gas on the product side in order to shift the equilibrium to the right. We then need low pressures, so the pressure temperature combination is low pressure. High temperature were then asked to calculate KP from K C. We know that K C given to us is 18 and to get KP, it's Casey multiplied by our T T for stage one is they're asking us to calculate it at 800 degrees Celsius. So to get Kelvin it'll be 800 plus the 2 73 And then we need to raise that whole thing to Delta End and Delta. And for stage one is going to be four minus two or just two. Well, then get a K P value of 140,000. Then the next step is using this KP value and knowing we have initial concentrations of methane and steam at 15 atmospheres, can we calculate the pressures of all of the gases at equilibrium? To do this will set up a nice table where we will assume that the initial concentrations of carbon monoxide and hydrogen gas are both zero, and the 15 atmospheres of methane and steam was given to us. As this reaction shifts, we're going to get minus X and minus X on our steam will get plus X on carbon monoxide and plus three X because of the three coefficient on hydrogen, then at equilibrium will have 15 minus x 15 minus x X and three x These being our equilibrium pressures now to solve for the pressures at equilibrium. We then need to solve for X so we can plug it into each one of these expressions in order to get our pressures for each of them. So KP then will be equal to the pressure of meth of carbon monoxide, which is X ah, the pressure of let's see the pressure of hydrogen gas, which is three X And then we're going to Cube that then to save space. And some time will just solve for X, using a program like Mathematica, your calculator or solver and excel, and we'll get X equal to 12.7. Now that we know that X is equal to 12.7, then we can use it to solve for all of the final pressures as a function of X carbon monoxide then is 12.7. Hydrogen gas is 12.7 times three or 38 point to a T M, and then both methane and water vapour will be 15 minus 12.7 or 2.3

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