The rate of disappearance of HCl was measured for the following reaction: CH3OH1aq2 + HCl1aq2¡CH3Cl1aq2 + H2O1l2 The following data were collected: Time (min) 3HCl 4 1M2 0.0 1.85 54.0 1.58 107.0 1.36 215.0 1.02 430.0 0.580 (c) Which is greater, the average rate between t = 54.0 and t = 215.0 min, or between t = 107.0 and t = 430.0 min?

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1. Identify the formula for the average rate of disappearance of a reactant, which is given by: \( \text{Average Rate} = -\frac{\Delta [\text{HCl}]}{\Delta t} \), where \( \Delta [\text{HCl}] \) is the change in concentration of HCl and \( \Delta t \) is the change in time.
2. Calculate \( \Delta [\text{HCl}] \) for the time interval between \( t = 54.0 \) min and \( t = 215.0 \) min. Use the concentrations at these times: \( [\text{HCl}]_{54.0} = 1.58 \) M and \( [\text{HCl}]_{215.0} = 1.02 \) M.
3. Calculate \( \Delta t \) for the time interval between \( t = 54.0 \) min and \( t = 215.0 \) min, which is \( 215.0 - 54.0 \) min.
4. Calculate the average rate for the interval between \( t = 54.0 \) min and \( t = 215.0 \) min using the formula from step 1.
5. Repeat steps 2-4 for the time interval between \( t = 107.0 \) min and \( t = 430.0 \) min, using the concentrations \( [\text{HCl}]_{107.0} = 1.36 \) M and \( [\text{HCl}]_{430.0} = 0.580 \) M, and compare the two average rates to determine which is greater.

Key Concepts

Reaction Rate

The reaction rate is a measure of how quickly reactants are converted into products in a chemical reaction. It can be expressed as the change in concentration of a reactant or product over time. Understanding how to calculate the average rate of reaction over specific time intervals is crucial for analyzing kinetic data.

Average Rate Calculation

The average rate of a reaction over a given time interval can be calculated by taking the difference in concentration of a reactant or product at the start and end of the interval, divided by the time elapsed. This calculation allows for comparison of reaction rates over different periods, which is essential for determining which interval has a greater rate of disappearance of HCl in this case.

Concentration Units

Concentration is typically expressed in molarity (M), which is moles of solute per liter of solution. In this question, the concentration of HCl is given in molarity, and understanding how to interpret these values is important for calculating changes in concentration over time. This knowledge is necessary to accurately assess the average rates of reaction between the specified time intervals.