Sucrose (C₁2H₂2O₁1), which is commonly known as table sugar, reacts in dilute acid solutions to form two simple sugars, glucose and fructose, both of which have the formula C6H₁2O6. C₁₂H₂2O + H₂O 2 C₂H₁2O6 Time (min) [C₁₂H₂O₁] (M) 0.316 0 39 80 140 210 a) Is the reaction first or second order? b) What is the value of the rate constant? c) What is the first half-life? 0.274 0.238 0.190 0.146

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**Title: Understanding the Kinetics of Sucrose Hydrolysis**

**Introduction:**
Sucrose (C₁₂H₂₂O₁₁), commonly known as table sugar, reacts in dilute acid solutions to form two simple sugars, glucose and fructose. Both of these products have the formula C₆H₁₂O₆.

**Reaction:**
\[ C_{12}H_{22}O_{11} + H_2O \rightarrow 2 \, C_{6}H_{12}O_{6} \]

**Experimental Data:**

The table below shows the concentration of sucrose (C₁₂H₂₂O₁₁) as a function of time during the reaction:

| Time (min) | \( [C_{12}H_{22}O_{11}] \) (M) |
|------------|-------------------------------|
| 0          | 0.316                         |
| 39         | 0.274                         |
| 80         | 0.238                         |
| 140        | 0.190                         |
| 210        | 0.146                         |

**Analysis:**

a) **Is the reaction first or second order?** \_\_\_\_\_\_\_\_\_\_\_\_

b) **What is the value of the rate constant?** \_\_\_\_\_\_\_\_\_\_\_\_

c) **What is the first half-life?** \_\_\_\_\_\_\_\_\_\_\_\_

**Explanation:**

In order to determine the order of the reaction, we analyze how the concentration of sucrose changes over time. For a first-order reaction, the relationship between the concentration of reactant and time follows the equation:

\[ \ln [C_{12}H_{22}O_{11}] = -kt + \ln [C_{12}H_{22}O_{11}]_0 \]

whereas for a second-order reaction, it follows:

\[ \frac{1}{[C_{12}H_{22}O_{11}]} = kt + \frac{1}{[C_{12}H_{22}O_{11}]_0} \]

By plotting the appropriate graphs (ln [C₁₂H₂₂O₁₁] vs. time for first-order, and 1/[C₁₂H₂
Transcribed Image Text:**Title: Understanding the Kinetics of Sucrose Hydrolysis** **Introduction:** Sucrose (C₁₂H₂₂O₁₁), commonly known as table sugar, reacts in dilute acid solutions to form two simple sugars, glucose and fructose. Both of these products have the formula C₆H₁₂O₆. **Reaction:** \[ C_{12}H_{22}O_{11} + H_2O \rightarrow 2 \, C_{6}H_{12}O_{6} \] **Experimental Data:** The table below shows the concentration of sucrose (C₁₂H₂₂O₁₁) as a function of time during the reaction: | Time (min) | \( [C_{12}H_{22}O_{11}] \) (M) | |------------|-------------------------------| | 0 | 0.316 | | 39 | 0.274 | | 80 | 0.238 | | 140 | 0.190 | | 210 | 0.146 | **Analysis:** a) **Is the reaction first or second order?** \_\_\_\_\_\_\_\_\_\_\_\_ b) **What is the value of the rate constant?** \_\_\_\_\_\_\_\_\_\_\_\_ c) **What is the first half-life?** \_\_\_\_\_\_\_\_\_\_\_\_ **Explanation:** In order to determine the order of the reaction, we analyze how the concentration of sucrose changes over time. For a first-order reaction, the relationship between the concentration of reactant and time follows the equation: \[ \ln [C_{12}H_{22}O_{11}] = -kt + \ln [C_{12}H_{22}O_{11}]_0 \] whereas for a second-order reaction, it follows: \[ \frac{1}{[C_{12}H_{22}O_{11}]} = kt + \frac{1}{[C_{12}H_{22}O_{11}]_0} \] By plotting the appropriate graphs (ln [C₁₂H₂₂O₁₁] vs. time for first-order, and 1/[C₁₂H₂
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