7. One reaction involved in the formation of smog is:
NO(g) + O3(g) ==> O2(g) + NO2(g)
The rate of the reaction can be calculated using the following equation:
rate = k[O3]^x[NO]^y where x and y are both equal to 1.
a) What would be the effect on the rxn rate if the concentration of ozone is doubled?
b) What would be the effect on the rxn rate if the concentration of nitric acid is tripled?
c) What would be the effect on the rxn rate if the concentration of ozone is doubled and the concentration of nitric oxide is tripled?
To determine the effect on the reaction rate in each scenario, we need to understand the impact of changing the concentration of each reactant. The given reaction rate equation is:
rate = k[O3]^x[NO]^y
a) Effect of doubling ozone concentration:
If the concentration of ozone ([O3]) is doubled, we plug the new concentration into the rate equation:
rate = k[(2[O3])^x[NO]^y
As x = 1, we get:
rate = k[(2[O3])[NO]^y]
Simplifying:
rate = 2k[O3][NO]^y
Therefore, doubling the concentration of ozone will directly double the rate of the reaction, assuming all other factors remain constant.
b) Effect of tripling nitric oxide concentration:
If the concentration of nitric oxide ([NO]) is tripled, we substitute the new concentration into the rate equation:
rate = k[O3]^x[(3[NO])^y
As y = 1, we have:
rate = k[O3]^x[(3[NO])]
Simplifying:
rate = 3k[O3][NO]
Hence, tripling the concentration of nitric oxide will result in a threefold increase in the rate of the reaction, provided that other factors are held constant.
c) Effect of doubling ozone concentration and tripling nitric oxide concentration:
If both the concentrations of ozone and nitric oxide are changed simultaneously, we substitute these new values into the rate equation:
rate = k[(2[O3])^x][(3[NO])^y]
As both x and y are equal to 1, we obtain:
rate = k[(2[O3])][(3[NO])]
Simplifying:
rate = 6k[O3][NO]
Therefore, doubling the concentration of ozone and tripling the concentration of nitric oxide will result in a sixfold increase in the rate of the reaction, assuming other factors remain unchanged.