Nitric oxide (NO) can be removed from gas-fired power-plant emissions by reaction with methane as follows:

CH4(g) + 4NO(g) --> 2N2(g) + CO2(g) + 2H2O(g)

Complete the equation relating the rates for each of the following:

a) the rate of appearance of N2 to the rate of appearance of CO2
rate= ∆[N2]/∆t = ??/∆t

b)rate of appearance of CO2 to the rate of disappearance of NO
rate= ∆[CO2]/∆t = ??/∆t

c) rate of disappearance of CH4 to the rate of appearance of H2O
rate= -∆[CH4]/∆t = ??/∆t

a. I can't write a delta symbol. delta T will be dT.

rate = d[N2]/2*dT = d[CO2]/dT

b and c are done the same way except the disappearance is shown with a - sign.
rate = d[CO2]/dT = -d[NO]4*dT

they are saying that the d[CO2] for the d[CO2]/dT is wrong but I'm not sure why.

a) To relate the rate of appearance of N2 to the rate of appearance of CO2, we need to determine the stoichiometric coefficients of N2 and CO2 in the balanced chemical equation.

From the balanced equation: CH4(g) + 4NO(g) --> 2N2(g) + CO2(g) + 2H2O(g)

We can see that the stoichiometric coefficient of N2 is 2, and the stoichiometric coefficient of CO2 is 1.

Therefore, the ratio of the rates of appearance of N2 to CO2 is:

rate(N2) : rate(CO2) = 2 : 1

b) To relate the rate of appearance of CO2 to the rate of disappearance of NO, we need to determine the stoichiometric coefficients of CO2 and NO in the balanced chemical equation.

From the balanced equation: CH4(g) + 4NO(g) --> 2N2(g) + CO2(g) + 2H2O(g)

We can see that the stoichiometric coefficient of CO2 is 1, and the stoichiometric coefficient of NO is 4.

Therefore, the ratio of the rates of appearance of CO2 to the rate of disappearance of NO is:

rate(CO2) : rate(NO) = 1 : 4

c) To relate the rate of disappearance of CH4 to the rate of appearance of H2O, we need to determine the stoichiometric coefficients of CH4 and H2O in the balanced chemical equation.

From the balanced equation: CH4(g) + 4NO(g) --> 2N2(g) + CO2(g) + 2H2O(g)

We can see that the stoichiometric coefficient of CH4 is 1, and the stoichiometric coefficient of H2O is 2.

Therefore, the ratio of the rates of disappearance of CH4 to the rate of appearance of H2O is:

rate(CH4) : rate(H2O) = -1 : 2

Please note that the negative sign (-) in rate(CH4) indicates the disappearance of CH4.

To determine the rates for each of the given reactions, we can use the stoichiometric coefficients of the balanced chemical equation as conversion factors. The rate of a reaction can be expressed in terms of the change in concentration of the reactants or products over time. Let's calculate the rates for each reaction:

a) The rate of appearance of N2 to the rate of appearance of CO2:
In the given reaction, the stoichiometric coefficient of N2 is 2, and the stoichiometric coefficient of CO2 is also 2. This means that for every mole of N2 that appears, one mole of CO2 also appears. Hence, the rate of appearance of N2 is equal to the rate of appearance of CO2.
Rate of appearance of N2 = Rate of appearance of CO2

b) The rate of appearance of CO2 to the rate of disappearance of NO:
From the balanced chemical equation, we see that the stoichiometric coefficient of CO2 is 1 and the stoichiometric coefficient of NO is 4. This means that for every mole of CO2 that appears, four moles of NO disappear. Hence, the rate of appearance of CO2 is four times the rate of disappearance of NO.
Rate of appearance of CO2 = 4 * Rate of disappearance of NO

c) The rate of disappearance of CH4 to the rate of appearance of H2O:
In the given reaction, the stoichiometric coefficient of CH4 is 1, and the stoichiometric coefficient of H2O is 2. This means that for every mole of CH4 that disappears, two moles of H2O appears. Hence, the rate of disappearance of CH4 is equal to twice the rate of appearance of H2O.
Rate of disappearance of CH4 = 2 * Rate of appearance of H2O

Note that the rates in the answers above are given with the assumption that the reaction is being carried out under appropriate conditions and at a constant temperature.