A student studied the kinetics of the reaction of sodium hypochlorite and a vegetable dye by the method of pseudo order. He mixed 5 mL of a 0.67 M solution of NaOCl with 15 mL of a vegetable dye, he took a portion of the mixture and absorbance was measured at intervals of 20 seconds over a period of 10 minutes. Then he made a graphic with his date for ln (absorbance) vs. time and which resulted in a straight line with negative slope. The straight line equation was y = -0123 x + 12.20. Furthermore it is known that the reaction order with respect to NaOCl is 1. Using this data answer:

1. What is the order of the reaction with respect to the dye?
2. What are the initial concentrations of NaOCl and the dye in the reaction?
3. What is the rate constant and its units for the reaction between NaOCl and the dye?

To answer these questions, we need to analyze the given information and use the method of pseudo order. Let's break it down step by step.

1. What is the order of the reaction with respect to the dye?
In the pseudo order method, the order of the reaction can be determined by examining the slope of the straight line obtained from plotting the natural logarithm of the absorbance against time. In this case, the equation of the line is y = -0.123 x + 12.20, where y represents ln(absorbance) and x represents time.

Since the slope of the line represents the rate constant, the order of the reaction with respect to the dye can be determined by comparing its slope to the known order of the reaction with respect to NaOCl. If the slope of the line matches the known order of NaOCl, then the order of the reaction with respect to the dye is 1.

2. What are the initial concentrations of NaOCl and the dye in the reaction?
To determine the initial concentrations of NaOCl and the dye, we need to analyze the initial portion of the plot. Since the slope of the line represents the rate constant, we can use the y-intercept of the line, which is 12.20, to calculate the initial concentration of the dye (C0). The formula is:
y = -k * t + ln(C0)
12.20 = -0.123 * 0 + ln(C0)
C0 = e^(12.20)

The initial concentration of NaOCl can be calculated by considering the ratio of the initial volumes used for the reaction. In this case, we mixed 5 mL of a 0.67 M solution of NaOCl with 15 mL of a vegetable dye. Since the volumes are in the ratio of 1:3, we can calculate the initial concentration of NaOCl (CNaOCl) using the formula:
CNaOCl = (Volume of NaOCl / Total volume) * Concentration of NaOCl
CNaOCl = (5 mL / 20 mL) * 0.67 M

3. What is the rate constant and its units for the reaction between NaOCl and the dye?
The rate constant can be obtained from the equation of the line (y = -0.123 x + 12.20) by comparing it to the rate law of the reaction. In this case, the reaction order with respect to NaOCl is 1, so the rate law is: rate = k * [NaOCl]^1 * [dye]^1

Since the dye order is also 1, the rate constant (k) obtained from the equation of the line represents the overall rate constant for the reaction. In this case, the rate constant is -0.123. The units of the rate constant will depend on the overall rate law. Without additional information, it is not possible to determine the specific units.

Note: It is important to note that the rate constant obtained from this pseudo order method may differ from the actual rate constant due to variations in the experimental conditions and the approximation made by assuming a pseudo order for the dye.