Consider the following reaction:
2N2O(g)--->2N2(g) + O2(g)
a. express the rate of the reaction with respect to each of the reactants and products.
b.In the first 10.0 s of the reaction, .018 mol of O2 is produced in a reaction vessel with a volume of .250L. What is the average rate of the reaction over this time interval?
c. Predict the rate of change in the concentration of N2O over this time interval. In other words, what is
delta[N2O]/delta t ?
Rate=
-1/2(⌂[N2O]/⌂t)=1/2(⌂[N2]/⌂t)=⌂[O2]/⌂t
*⌂ is the delta sign
a. To express the rate of the reaction with respect to each of the reactants and products, we need to determine the coefficients of the balanced chemical equation. In this case, the coefficients are:
2N2O(g) → 2N2(g) + O2(g)
The rate of the reaction can be expressed as follows:
- Rate of the reaction with respect to N2O: -1/2 Δ[N2O] / Δt
- Rate of the reaction with respect to N2: 1/2 Δ[N2] / Δt
- Rate of the reaction with respect to O2: 1 Δ[O2] / Δt
b. The average rate of the reaction over the given time interval can be calculated using the formula:
Average rate = Change in concentration / Change in time
Given that 0.018 mol of O2 is produced in a reaction vessel with a volume of 0.250 L during the first 10.0 s, we can use this information to calculate the average rate of the reaction:
Average rate = (0.018 mol / 0.250 L) / 10.0 s
Note that the units of concentration and volume need to match for the calculation. In this case, mol and L are consistent. The resulting average rate will be in mol/(L·s).
c. To predict the rate of change in the concentration of N2O over the given time interval, we can use the stoichiometry of the reaction. From the balanced chemical equation, we can see that the coefficient of N2O is 2. This means that for every mole of N2O consumed, 1/2 mole of O2 is produced.
Therefore, the rate of change in the concentration of N2O can be calculated as:
Δ[N2O] / Δt = -0.5 * Δ[O2] / Δt
Since the average rate of O2 production over the given time interval is known, you can substitute this value into the equation to determine the rate of change in the concentration of N2O.
a. To express the rate of the reaction with respect to each of the reactants and products, we can use the stoichiometry of the balanced equation.
The balanced equation is:
2N2O(g) ---> 2N2(g) + O2(g)
The rate of the reaction with respect to each reactant or product is given by the coefficient in front of the species in the balanced equation. In this case:
- The rate of the reaction with respect to N2O is (-2) because it is consumed at a rate of 2 moles for every mole of reaction.
- The rate of the reaction with respect to N2 is (+2) because it is produced at a rate of 2 moles for every mole of reaction.
- The rate of the reaction with respect to O2 is (+1) because it is produced at a rate of 1 mole for every mole of reaction.
b. The average rate of the reaction over a given time interval can be calculated by dividing the change in the concentration of a reactant or product by the time interval.
In this case, we are given that 0.018 mol of O2 is produced in a reaction vessel with a volume of 0.250 L in the first 10.0 s of the reaction. To calculate the average rate of the reaction over this time interval, we need to convert the given information into concentration units.
Concentration (in mol/L) = Number of moles / Volume
Concentration of O2 = 0.018 mol / 0.250 L = 0.072 mol/L
Now we can calculate the average rate of the reaction:
Average rate = Change in concentration of O2 / Time interval = (0.072 mol/L - 0 mol/L) / 10.0 s = 0.0072 mol/(L·s)
Therefore, the average rate of the reaction over this time interval is 0.0072 mol/(L·s).
c. To predict the rate of change in the concentration of N2O over the given time interval, we can use the stoichiometry of the balanced equation and the information provided.
From the balanced equation 2N2O(g) ---> 2N2(g) + O2(g), we know that 2 moles of N2O react to produce 2 moles of N2 (and 1 mole of O2).
Since 0.018 mol of O2 is produced in the first 10.0 s, we can calculate the moles of N2O consumed by dividing by the stoichiometric ratio:
Moles of N2O consumed = (0.018 mol O2) / (1 mol O2 / 2 mol N2O) = 0.036 mol N2O
Now, we divide the change in concentration of N2O by the time interval to get the rate of change:
Rate of change in concentration of N2O = Change in concentration of N2O / Time interval = (0.036 mol / 0.250 L) / 10.0 s = 0.144 mol/(L·s)
Therefore, the rate of change in the concentration of N2O over this time interval is 0.144 mol/(L·s), or delta[N2O]/delta t = 0.144 mol/(L·s).