Calculate K c for: C(s) + ½ O 2 (g) + H 2 (g) ⇌ ½ CH 3 OH(g) + ½ CO(g) K c = ? Given the following reactions: 4 C(s) + 2 O 2 (g) ⇌ 4 CO(g) K p = 2.11 x 10 43 CH 3 OH(g) + H 2 O(g) ⇌ CO 2 (g) + 3 H 2 (g) K p = 7.17 x 10 –2 CO(g) + H 2 O(g) ⇌ CO 2 (g) + H 2 (g) K p = 2.00 x 10 3

In this question we're told to calculate kc for the equation of carbon solid reacting with half a mole of oxygen gas plus 1 mole of hydrogen gas to produce half a mole of methanol gas plus half a mole of carbon monoxide gas. Alright. So here we need to figure out what kc is for this, but notice that we're given kp for all these partial reactions. What equation connects kp and kc? Well remember, kp equals kcrT to the delta n And here we're not giving temperature, so we can assume that we're dealing with, temperature under standard conditions which is typically 25 degrees Celsius. So we add 273.15 to this, And we're gonna say our R is our gas constant which is, 0.0206 times 298.15 Kelvin. Remember I added 273.15 to my standard conditions of 25 degrees Celsius. Delta n is our moles of product, gaseous product minus my moles of gaseous reactants. So how many moles of product do we have as gas? We have half and a half which is 1, minus, solid doesn't count, we have half plus 1, so 1.5 moles of gas is reacted, so this is negative 0.5. For us to find KC, we need to know what KP is because that's the other missing variable. To find k p we're going to use our overall reaction, look at it and see where each one of those compounds are found within our partial reactions. So let's go 1 by 1 and see where we can find them. Here we have carbon solid, we need carbon solid, one mole of it as a reactant. If we look at our 3 partial reactions we can see the only place I see carbon solid is right here. They have to match exactly. The partial reaction one has 4 moles of their of carbon solid, so that means we have to divide this equation by 4 to get rid of it. So that will give us C solid plus, so divide 2 by 4 gives me half, half o two. And divide 4 that give me 1 Cl gas. Remember when we divide by a number, so this means that the new KP will be to the 1 fourth. K. It's the reciprocal of the factor. So it's 2.11 times 10 to the 43rd to the 1 fourth power. If you do that correctly you should get 6.77 5, oops, 7775 times 10 to the 10. This is now all gone because it's been changed into this new equation. So this first one is done. Next we have to find o2. Well where do we find o2 within our partial reactions? Well, we see O2 here, but we also see let's see is that the only place we see O2? That looks like the only place we see O2, so we're good. And, they match already. We have half O2 here as a reactant to match up with this half O2 here as reactant. Next, H2 gas, where do we see H2? H2, we see it here and we see it here. Remember, if you find the compound in multiple partial reactions we skip it. Next, we need half a mole of methanol gas. So here goes methanol gas, there's 2 changes I need to do. 1st, it needs to be a product just like in this overall reaction, and we need half of it. We need half a mole not 1 whole mole. So the two changes that I need to do are reverse, so we need a reversal, and divide by 2. Okay, so then we're going to have here half CO2 gas plus 3 over 2 H2 gas, gives me half Methanol Alcohol as a gas plus half H2O gas. When I reverse it, that's gonna give me the inverse, and then I'm dividing it by 2 so that's gonna raise to the half power. When we do that our new kp will be 3.73457. Now what's next? We need half a mole of carbon monoxide gas. Right. Remember this is now gone, been converted. So where do we see half a mole of carbon monoxide gas? Well carbon monoxide is found in 2 places, it's found here, but it's also found here. We have to say to ourselves, okay, I need to have half a mole of it as a product. This part already is a product, but there's 1 mole of it. We need half a mole. That tells me that I should do this, I should divide this equation by 2. Because doing so, divided by 2, we'll see what effect that has. Dividing it by 2 gives me half CO gas plus half H2O gas, and it's gonna produce half CO2 gas, plus half H2 gas. Then k p is now to the half power. Alright, so we're gonna say here that's 2.00 times 10 to the 3 to the half, that comes out to be 44.721. Alright. So we got our 3 new KP values. This one, this one, and this one. Let's cancel out our intermediates. Alright. So what's going to cancel out here? Let's see. So all half of this is gonna cancel with half of this leaving us with half. Cool. What else cancels out? Half of this CO two is reacting, cancel out with this half that's a product. Let's see. Half of this h two cancels out with half of this h two, this is 1.53 over 2 is 1.5, so we've lost half, leaving us with one left. Okay. What else can cancel out from here? Let's see here. Okay. So CS solid comes down, half o two comes down. What else? Oh, half water. One's a product, one's a reacting they totally cancel out. When we look what is left behind we have 1 mole of carbon solid as a reactant, half a mole of o2 as a reactant, 1 mole of H2 as a reactant, which matches up with the 3 reactants from our overall reaction. Then we have half a mole of methanol gas, and then we have what else? What's the last thing? Half a mole of carbon monoxide gas. So we have we've just recreated our overall reaction, so we know we've done it correctly. This tells me that all I need to do now is multiply these 3 KP's for my partial reactions to get the overall KP. So when I multiply those 3 together, okay, so again I'm just going to multiply these 3 together, 10 to 10, times 3.73457 times 44.721. When I do that I'm gonna get 1.1319 times 10 to the 13. There goes my kp for the overall reaction. Since I know my overall kp I can come back to the equation where that connects kp and kc together. So, that's 1.1319 times 10 to the 13. All I have to do here is isolate KC. So you're dividing out this rt to the negative 0.5 on both sides to isolate KC. When we do that, I'm going to write it down here, when I do that I'll get my kc as being 5 point and here we're gonna do it to 3 sig figs, 5.60x1013. This here would represent the kc of my overall reaction.

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16. Chemical Equilibrium

Calculating K For Overall Reaction

General Chemistry

16. Chemical Equilibrium

Calculating K For Overall Reaction

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Multiple Choice

Calculate K_c for: C(s) + ½ O₂(g) + H₂(g) ⇌ ½ CH₃OH(g) + ½ CO(g) K_c = ?
Given the following reactions:
4 C(s) + 2 O₂(g) ⇌ 4 CO(g) K_p = 2.11 x 10⁴³
CH₃OH(g) + H₂O(g) ⇌ CO₂(g) + 3 H₂(g) K_p = 7.17 x 10^–2
CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g) K_p = 2.00 x 10³

1.13×10¹³

5.60×10¹³

1.37×10¹⁵

5.35×10¹³

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Verified step by step guidance

Identify the target reaction: C(s) + ½ O2(g) + H2(g) ⇌ ½ CH3OH(g) + ½ CO(g). We need to find the equilibrium constant Kc for this reaction.

Examine the given reactions and their equilibrium constants (Kp values): 1) 4 C(s) + 2 O2(g) ⇌ 4 CO(g) with Kp = 2.11 x 10^4, 2) CH3OH(g) + H2O(g) ⇌ CO2(g) + 3 H2(g) with Kp = 7.17 x 10^-2, 3) CO(g) + H2O(g) ⇌ CO2(g) + H2(g) with Kp = 2.00 x 10^3.

Use Hess's Law to manipulate the given reactions to derive the target reaction. This involves reversing, multiplying, or dividing the reactions and adjusting their Kp values accordingly.

Convert Kp to Kc using the relation Kc = Kp(RT)^Δn, where Δn is the change in moles of gas between products and reactants, R is the gas constant, and T is the temperature in Kelvin. Assume standard conditions if not specified.

Combine the adjusted Kp values from the manipulated reactions to find the Kc for the target reaction. This involves multiplying the Kp values of the individual steps to get the overall Kc.