Consider the reaction below:
Cgraphite(s) + F2(g) +1/2O2(g) → CF2O(g)
Which of the following is a correct rate expression?
1. rate = −2∆[O2]/∆t
2. rate = −∆[CF2O]/∆t
3. rate =∆[F2]/∆t
4. rate = −∆[Cgraphite]/∆t
5. rate =∆[Cgraphite]/∆t
4 and 5 can't be right because graphite is a solid.
3 isn't right because it must have a - sign.
2 isn't right because the sign is +.
That leaves 1 for the right answer.
The rate = 1/(1/2)dO2/dt which is 2dO2/dt.
To determine the correct rate expression for the given reaction, we need to examine the stoichiometry of the reaction. The balanced equation tells us that one mole of Cgraphite reacts with one mole of F2 and one-half mole of O2 to produce one mole of CF2O.
Based on the stoichiometry, the rate of the reaction is related to the change in concentration of the reactants or products over time.
Looking at the options provided:
1. rate = −2∆[O2]/∆t: This option incorrectly includes a factor of 2 in the rate expression for O2, which is not in agreement with the stoichiometry. Therefore, it is incorrect.
2. rate = −∆[CF2O]/∆t: This option correctly represents the change in concentration of CF2O over time, according to the stoichiometry. It is the correct rate expression.
3. rate =∆[F2]/∆t: This option represents the change in concentration of F2, but it does not account for the stoichiometry of the reaction. Therefore, it is incorrect.
4. rate = −∆[Cgraphite]/∆t: This option correctly represents the change in concentration of Cgraphite over time, according to the stoichiometry. It is also a correct rate expression.
5. rate =∆[Cgraphite]/∆t: This option represents the change in concentration of Cgraphite, but it does not include the negative sign, which indicates the consumption of the reactant. Therefore, it is incorrect.
So, based on the above analysis, options 2 and 4 are correct rate expressions for the given reaction.
To determine the correct rate expression for the given reaction, we must examine the balanced chemical equation. The coefficients in the balanced equation represent the stoichiometry of the reaction and can be used to determine the rate expression.
The balanced chemical equation for the reaction is:
Cgraphite(s) + F2(g) + 1/2O2(g) → CF2O(g)
From the balanced equation, we can see that 1 mole of Cgraphite reacts with 1 mole of F2 and 1/2 mole of O2 to produce 1 mole of CF2O.
Therefore, the rate expression can be determined by comparing the change in concentration of reactants or the buildup of products with respect to time. To do this, we examine the coefficients of the reactant or product involved in the rate-determining step.
Looking at the balanced equation, we see that the coefficient of O2 is 1/2. Therefore, the rate expression involving O2 can be expressed as:
rate = -2∆[O2]/∆t
However, it is important to note that this rate expression is negative because O2 is being consumed in the reaction.
Therefore, the correct rate expression for the given reaction is:
1. rate = -2∆[O2]/∆t