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Difficulty: EasyRate of Reaction and Collision Theory

During a chemical reaction between zinc metal and dilute hydrochloric acid, the volume of hydrogen gas produced was recorded over time. At 10 s10\text{ s}, the total volume of hydrogen gas collected was 15.0 cm315.0\text{ cm}^3, and at 30 s30\text{ s}, the volume collected reached 45.0 cm345.0\text{ cm}^3. What is the average rate of hydrogen gas evolution in cm3 s−1\text{cm}^3\text{ s}^{-1} over this 20-second20\text{-second} time interval?

Answer: 1.5 cm³ s⁻¹

Answer

The average rate of evolution of hydrogen gas over the time interval is 1.5 cm3 s−11.5\text{ cm}^3\text{ s}^{-1}.
The average rate of reaction is calculated by dividing the volume of gas produced during the interval (ΔV=45.0 cm3−15.0 cm3=30.0 cm3\Delta V = 45.0\text{ cm}^3 - 15.0\text{ cm}^3 = 30.0\text{ cm}^3) by the elapsed time (Δt=30 s−10 s=20 s\Delta t = 30\text{ s} - 10\text{ s} = 20\text{ s}), yielding 1.5 cm3 s−11.5\text{ cm}^3\text{ s}^{-1}.

Step-by-Step Solution

1
Determine the volume of hydrogen gas evolved during the specified time interval.
ΔV=45.0 cm3−15.0 cm3=30.0 cm3\Delta V = 45.0\text{ cm}^3 - 15.0\text{ cm}^3 = 30.0\text{ cm}^3
The volume change represents the quantity of product formed specifically between 10 s10\text{ s} and 30 s30\text{ s}.
2
Determine the time elapsed over the interval.
Δt=30 s−10 s=20 s\Delta t = 30\text{ s} - 10\text{ s} = 20\text{ s}
The reaction rate is measured over the duration between the two observations.
3
Compute the average rate of gas evolution.
\text{Rate} = \frac{\Delta V}{\Delta t} = \frac{30.0\text{ cm}^3}{20\text{ s}} = 1.5\text{ cm}^3\text{ s}^{-1}
The average rate of reaction with respect to gas volume is defined as the change in volume per unit time.

Key Concept

Average Rate of Reaction
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Topics

Rate of Reaction and Collision Theory