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At 25^(@)C, pH range of phenolphthalein ...

At `25^(@)C, pH` range of phenolphthalein is `8-10`. At `100^(@)C `, ` pH` range of phenolphthalein would be

A

pH range remain unaffected by the temperature

B

pH range is altered to 8 -9

C

pH range is altered to 7-11

D

pH range is altered to 8-11

Text Solution

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The correct Answer is:
To determine the pH range of phenolphthalein at 100°C, we can follow these steps: ### Step 1: Understand the pH range of phenolphthalein at 25°C The pH range of phenolphthalein at 25°C is given as 8 to 10. This means that phenolphthalein changes color in this pH range. ### Step 2: Relate pH to pKa The pH range of an indicator can be expressed in terms of its pKa value. The formula for the pH range of an indicator is: \[ \text{pH range} = \text{pK}_a \pm 1 \] For phenolphthalein, at 25°C: - The lower limit (pH = 8) corresponds to: \[ \text{pK}_a - 1 = 8 \] Hence, \( \text{pK}_a = 9 \). - The upper limit (pH = 10) corresponds to: \[ \text{pK}_a + 1 = 10 \] This confirms \( \text{pK}_a = 9 \). ### Step 3: Consider the effect of temperature on pKa As temperature increases, the equilibrium constant (K) for the dissociation of the indicator increases. This means that the pKa value decreases with an increase in temperature. ### Step 4: Estimate the change in pKa While the exact change in pKa with temperature can vary, a general rule is that the pKa decreases by approximately 1 unit for every 10°C increase in temperature. Since we are increasing the temperature from 25°C to 100°C (a change of 75°C), we can estimate the change in pKa: - Decrease in pKa = \( \frac{75}{10} = 7.5 \) ### Step 5: Calculate the new pKa at 100°C Starting from the original pKa of 9 at 25°C: \[ \text{New pK}_a = 9 - 7.5 = 1.5 \] ### Step 6: Determine the new pH range Using the new pKa value, we can find the new pH range: - Lower limit: \[ \text{pH} = \text{pK}_a - 1 = 1.5 - 1 = 0.5 \] - Upper limit: \[ \text{pH} = \text{pK}_a + 1 = 1.5 + 1 = 2.5 \] Thus, the pH range of phenolphthalein at 100°C is approximately 0.5 to 2.5. ### Final Answer The pH range of phenolphthalein at 100°C would be approximately 0.5 to 2.5. ---
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