To find the change in pH (ΔpH) when 100 ml of 0.01 M HCl is added to a solution containing 0.1 millimoles of NaHCO₃, we can follow these steps:
### Step 1: Calculate the number of moles of HCl
Given:
- Volume of HCl = 100 ml = 0.1 L
- Concentration of HCl = 0.01 M
Using the formula:
\[
\text{Number of moles} = \text{Volume (L)} \times \text{Concentration (M)}
\]
\[
\text{Number of moles of HCl} = 0.1 \, \text{L} \times 0.01 \, \text{mol/L} = 0.001 \, \text{mol} = 1 \, \text{mmol}
\]
### Step 2: Determine the reaction between HCl and NaHCO₃
The reaction between hydrochloric acid (HCl) and sodium bicarbonate (NaHCO₃) can be represented as:
\[
\text{HCl} + \text{NaHCO}_3 \rightarrow \text{NaCl} + \text{H}_2\text{CO}_3
\]
From the reaction, we see that 1 mmol of HCl reacts with 1 mmol of NaHCO₃.
### Step 3: Calculate the remaining moles after the reaction
Given:
- Initial moles of NaHCO₃ = 0.1 mmol = 0.1 mmol
Since we have 1 mmol of HCl and 0.1 mmol of NaHCO₃, all of the NaHCO₃ will react, and we will have:
\[
\text{Remaining moles of HCl} = 1 \, \text{mmol} - 0.1 \, \text{mmol} = 0.9 \, \text{mmol}
\]
### Step 4: Calculate the concentration of H⁺ ions in the final solution
The total volume of the solution after adding HCl is approximately:
\[
\text{Total volume} = 100 \, \text{ml} + \text{negligible volume} \approx 100 \, \text{ml} = 0.1 \, \text{L}
\]
The concentration of H⁺ ions can be calculated as:
\[
\text{Concentration of H}^+ = \frac{\text{Remaining moles of HCl}}{\text{Total volume}} = \frac{0.9 \, \text{mmol}}{0.1 \, \text{L}} = 0.009 \, \text{mol/L} = 9 \times 10^{-3} \, \text{M}
\]
### Step 5: Calculate the final pH
Using the formula for pH:
\[
\text{pH} = -\log[\text{H}^+]
\]
Substituting the concentration of H⁺ ions:
\[
\text{pH} = -\log(9 \times 10^{-3}) = -\log(9) - \log(10^{-3}) = -\log(9) + 3
\]
Using the approximation \(\log(9) \approx 0.954\):
\[
\text{pH} = -0.954 + 3 = 2.046
\]
### Step 6: Calculate the initial pH of the NaHCO₃ solution
NaHCO₃ is a weak base, and its pH can be calculated using its equilibrium with HCO₃⁻. However, for simplicity, we can assume that the initial pH of a 0.1 mmol NaHCO₃ solution is around 8.4 (since it is a weak basic solution).
### Step 7: Calculate ΔpH
Finally, we can find the change in pH:
\[
\Delta \text{pH} = \text{Final pH} - \text{Initial pH} = 2.046 - 8.4 = -6.354
\]
### Conclusion
The change in pH (ΔpH) when 100 ml of 0.01 M HCl is added to a solution containing 0.1 mmol of NaHCO₃ is approximately -6.354.
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