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
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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Chapter11: Chemical Kinetics
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe47599a4-201e-4a21-820b-be4e0f71610f%2F5e980047-f4b9-4450-a0a3-c8ff6da6081c%2F3lvurfbu_processed.jpeg&w=3840&q=75)
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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