Hydrogen iodine is a strong acid that is used in chemical synthesis to produce some common drugs as well as a source for iodine, I2. Data for the formation of hydrogen iodine was obtained as shown. The reaction was found to be first order with respect to hydrogen gas and iodine.
H2(g)+I2(g)-->2HI(g)
Rate=k[H2][I2]
[I2](M) time
0.1 time 0s
0.0956 time 100s
0.0916 time 200s
0.0879 time 300s
1. Write the rate equations for the relative rate of dissaperance of hydrogen gas and iodine and the appearance of hydrogen iodide.
2. If the rate of disappearance of iodine vapor is 0.0250M/s, what is the rate of appearance of hydrogen iodide?
To determine the rate equations, we need to analyze the given data and observe how the concentrations change over time. Since the reaction is first order with respect to both hydrogen gas (H2) and iodine (I2), the rate equations can be written as:
Rate of disappearance of hydrogen gas (H2): d[H2]/dt = -k[H2][I2]
Rate of disappearance of iodine (I2): d[I2]/dt = -k[H2][I2]
Rate of appearance of hydrogen iodide (HI): d[HI]/dt = 2k[H2][I2]
Note that the negative sign indicates the decrease in concentration of the reactants (disappearance) and the positive sign indicates the increase in concentration of the product (appearance).
To answer the second question, we can use the rate equation for the disappearance of iodine (d[I2]/dt = -k[H2][I2]) and substitute the given rate (-0.0250 M/s) for the rate of disappearance of iodine. We can then solve for the rate of appearance of hydrogen iodide (d[HI]/dt).
Given: d[I2]/dt = -0.0250 M/s
By rearranging the rate equation, we have:
-0.0250 M/s = -k[H2][I2]
Since we don't know the concentrations of H2 and I2, we cannot directly solve for k. However, we can use the data provided to determine the value of k.
Let's consider the data point at 0s:
[I2] = 0.1 M
[H2] = ?
Plugging this data into the rate equation for the disappearance of iodine (d[I2]/dt = -k[H2][I2]), we get:
-0.0250 M/s = -k[H2](0.1 M)
Solving for [H2], we have:
[H2] = -0.0250 M/s / (k * 0.1 M)
Now, we can use the above concentration of H2 to calculate the rate of appearance of hydrogen iodide (d[HI]/dt) using the rate expression: d[HI]/dt = 2k[H2][I2].
Substituting the values, we get:
d[HI]/dt = 2k(-0.0250 M/s / (k * 0.1 M))(0.1 M)
Now, simplify and solve for d[HI]/dt to get the rate of appearance of hydrogen iodide.