Q.1. In the reaction between NO2 and HCl, which yield NOCl, Cl2 and water the initial rate of reaction (p) at 55 degree was measured at various pressures of NO2 with HCl pressure kept constant. PNO2/torr 7.4 7.5 8.6 12.3 14.8 17.5 24.3 Initial rate (p) 1.12 1.48 1.62 3.2 4.4 6.6 13.8 Hence determine the reaction order with respect to NO2.

To determine the reaction order with respect to NO2 in the reaction between NO2 and HCl, we can analyze the initial rates of reaction at varying pressures of NO2 while keeping the pressure of HCl constant. The data provided gives us a clear path to follow using the method of initial rates.

Understanding Reaction Order

The reaction order with respect to a reactant indicates how the rate of reaction changes as the concentration (or pressure, in this case) of that reactant changes. For a reaction of the form:

aA + bB → products

The rate law can be expressed as:

Rate = k[A]^m[B]^n

Where:

• k is the rate constant.
• [A] and [B] are the concentrations (or pressures) of the reactants.
• m and n are the orders of the reaction with respect to A and B, respectively.

Analyzing the Data

Given the pressures of NO2 and the corresponding initial rates:

• PNO2 (torr): 7.4, 7.5, 8.6, 12.3, 14.8, 17.5, 24.3
• Initial Rate (p): 1.12, 1.48, 1.62, 3.2, 4.4, 6.6, 13.8

Calculating Reaction Order

To find the order with respect to NO2, we can use the method of comparing the rates at different pressures. We will take two sets of data points and apply the rate law concept:

Let’s consider the data points for PNO2 = 7.4 torr and PNO2 = 14.8 torr:

• At 7.4 torr: Rate = 1.12
• At 14.8 torr: Rate = 4.4

Using the rate law, we can set up the following ratio:

Rate1 / Rate2 = (PNO2,1)^m / (PNO2,2)^m

Substituting the values:

1.12 / 4.4 = (7.4)^m / (14.8)^m

Calculating the Ratio

First, calculate the left side:

1.12 / 4.4 = 0.2545

Now, for the right side:

(7.4 / 14.8)^m = (0.5)^m

Setting Up the Equation

Now we have:

0.2545 = (0.5)^m

Solving for m

To solve for m, we can take the logarithm of both sides:

log(0.2545) = m * log(0.5)

Calculating the logarithms:

• log(0.2545) ≈ -0.594
• log(0.5) ≈ -0.301

Now substituting these values:

-0.594 = m * (-0.301)

Solving for m gives:

m ≈ 1.97

Conclusion on Reaction Order

Since the order of reaction must be a whole number, we can round 1.97 to 2. Therefore, the reaction is second order with respect to NO2. This means that if the pressure of NO2 is doubled, the rate of reaction will increase by a factor of four, illustrating the quadratic relationship between the concentration of NO2 and the rate of reaction.