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For the reaction$$\mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$the equilibrium constant, $K$ , has the value $5.21 \times 10^{-3}$ at a particular temperature. If the system is analyzed at equilibrium at this temperature, it is found that $[\mathrm{CO}(g)]=4.73 \times 10^{-3} M,\left[\mathrm{H}_{2} \mathrm{O}(g)\right]=5.21 \times 10^{-3} \mathrm{M}$ , and $\left[\mathrm{CO}_{2}(g)\right]=3.99 \times 10^{-2} \mathrm{M}$ . What is the equilibriumconcentration of $\mathrm{H}_{2}(g)$ in the system?
$\left[H_{2}\right]=0.119 M$
Chemistry 102
Chapter 17
Equilibrium
Section 8
Applications Involving the Equilibrium Constant
Chemical Equilibrium
University of Central Florida
University of Toronto
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So looking at this problem, we're gonna be looking at how to find equilibrium, concentration of hydrogen. And I've written out the problem here. An ever not the respective concentrations for each is was the casar you for the reaction. So really solving for this concentration starting off were to write out a K Q equation and we look for solids and liquids. Let me see that there are none. So moving on will have the products in the numerator. So it's rate, See oh, and H 20 and the reactions of the denominator and booth water. So putting you are the values we have My point, too, to negative three is equal to 4.73 times 10 to predictive three times 5.21 times 10 to the negative three. And in the denominator, we have great way 99 times 10 to the negative, too times. So, sultan crags, we're gonna multiply these two now I used together and doing that should get. And we're also gonna multiply these $2 together just a simplify. So doing nothing should get 2.8 times 10 to the negative four x this equal to 2.46 times 10 to the negative. Five. Got that? Because we did 3.99 times 10 to the negative two times X. And then we're gonna cross multiply, so kind of act like there's one over here. But I'm also quite times this and multiply and multiply these two together. And those two together you will come up with this. So 2.8 times 10 the negative for X her to 2.46 times sent a five those sulfur x we're gonna defied inside times to quit. We'll eat incentive to get it for and doing that X should be one 0.119 And that's how you saw for
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