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Problem 53 Medium Difficulty

What is the value of the equilibrium constant at $500^{\circ} \mathrm{C}$ for the formation of $\mathrm{NH}_{3}$ according to the following equation?
$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$
An equilibrium mixture of $\mathrm{NH}_{3}(g), \mathrm{H}_{2}(g),$ and $\mathrm{N}_{2}(g)$ at $500^{\circ} \mathrm{C}$ was found to contain $1.35 \mathrm{M} \mathrm{H}_{2}, 1.15 \mathrm{M}_{2},$ and 4.12 $\times 10^{-1} M \mathrm{NH}_{3}$

Answer

$6.00 \times 10^{-2}$

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Chemistry 102

Chemistry

Chapter 13

Fundamental Equilibrium Concepts

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Video Transcript

So here we're asked to consider the equilibrium between nitrogen and hydrogen gas and ammonia, and we're told that at equilibrium in a temperature of 500 degrees Celsius, the concentrations of each of these species are written down here below the equation, and they want us to calculate the value of equilibrium constant at this given temperature. What that means is that since we know that these concentrations represent the reaction vessel at equilibrium, we know that we could just write the equilibrium expression, plug these values into it and calculate the equilibrium constant. So we know that Casey is going to be equal to the concentration of products over reactions. So here we're going to have the concentration of ammonia squared, divided by the concentration of nitrogen and the concentration of hydrogen hydrogen to the third. So we're really just going to be plugging our values and for this So we're going to have a 0.412 square to the numerator, and we're going to have 1.15 times 1.35 to the third in the denominator when we multiply this through, what we find is that the equilibrium constant for this expression is six times 10 to the negative, too

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Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson

Chemistry

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