Question 13 of 37intermediate🔧 ApplyShort Answer2 marks

The decomposition of dimethyl ether leads to the formation of CH4\text{CH}_4, H2\text{H}_2 and CO\text{CO} and the reaction rate is given by Rate =k[CH3OCH3]3/2= k[\text{CH}_3\text{OCH}_3]^{3/2}. The rate of reaction is followed by increase in pressure in a closed vessel, so the rate can also be expressed in terms of the partial pressure of dimethyl ether, i.e., Rate =k(pCH3OCH3)3/2= k\left(p_{\text{CH}_3\text{OCH}_3}\right)^{3/2}. If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?

Correct Answer

Units of rate: bar min⁻¹

Units of rate constant: bar⁻¹/² min⁻¹

Calculation:

Step 1: Determine units of rate Since the rate is expressed in terms of partial pressure and pressure is measured in bar while time is in minutes: Rate = Change in pressure / Time Units of rate = bar min⁻¹

Step 2: Determine units of rate constant Given: Rate = k(p)^(3/2) Rearranging: k = Rate / (p)^(3/2) Substituting units: k = (bar min⁻¹) / (bar)^(3/2) k = bar^(1 - 3/2) min⁻¹ k = bar^(-1/2) min⁻¹ k = bar⁻¹/² min⁻¹

Exercise: EXERCISES | Q: 3.4 | (Page 25)
For More Understanding

Explanation

This question tests understanding of units in chemical kinetics when rate is expressed in terms of partial pressure instead of concentration. The order of reaction is 3/2. For rate expressed in pressure terms, the unit is pressure/time (bar min⁻¹). The rate constant unit depends on the order: k = Rate/(pressure)^n, giving bar^(1-n) min⁻¹. For n = 3/2, this yields bar^(-1/2) min⁻¹.

Solution Steps

  1. Step 1: Rate = pressure/time, so units = bar min⁻¹

  2. Step 2: From Rate = k(p)^(3/2), rearranging gives k = Rate/(p)^(3/2)

  3. Step 3: Substituting units: k = (bar min⁻¹)/(bar)^(3/2) = bar^(-1/2) min⁻¹

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