1. To write the rate equations for the relative rate of disappearance of hydrogen gas and iodine, and the appearance of hydrogen iodide, we can use the stoichiometric coefficients from the balanced chemical equation.
The balanced chemical equation for the reaction is:
H2(g) + I2(g) --> 2HI(g)
The rate equation for the disappearance of hydrogen gas (H2) would be:
Rate(H2) = -k[H2][I2]
The rate equation for the disappearance of iodine (I2) would be:
Rate(I2) = -k[H2][I2]
The rate equation for the appearance of hydrogen iodide (HI) would be:
Rate(HI) = +2k[H2][I2]
2. If the rate of disappearance of iodine vapor is given as 0.0250 M/s, we can use the rate equation for iodine to find the rate of appearance of hydrogen iodide.
From the rate equation for iodine (Rate(I2) = -k[H2][I2]), we can determine the value of k by using the given data:
[I2] (M) time (s)
0.1 0s
0.0956 100s
0.0916 200s
0.0879 300s
Let's use the data at 0s and 100s to calculate the rate constant (k):
Rate(I2) = (0.0956 M - 0.1 M) / (100s - 0s) = -0.00044 M/s
Now, we can substitute the given rate of disappearance of iodine (Rate(I2) = -0.0250 M/s) into the rate equation for iodine and solve for k:
-0.0250 M/s = -k[H2](0.1 M)
By rearranging the equation, we can find the value of k:
k = 0.0250 M/s / (0.1 M) = 0.25 1/s
Now that we have the value of k, we can calculate the rate of appearance of hydrogen iodide (Rate(HI)) using the rate equation for HI (Rate(HI) = +2k[H2][I2]):
Rate(HI) = +2 * 0.25 1/s * (0.1 M) * (0.0250 M/s) = 0.00125 M/s
Therefore, the rate of appearance of hydrogen iodide is 0.00125 M/s.