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Solution Concentration and pH Calculations

CSCA Solution Concentration and pH Calculations study guide organized around the publicly available CSCA syllabus. Practice Chemistry questions on aicsca.com.

Before planning this topic, check the CSCA Exam Guide 2026 for exam dates, registration, fees, and subject requirements.

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This study guide is organized around the publicly available CSCA syllabus for international undergraduate applicants.

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International students preparing for CSCA Math, Physics, Chemistry, or Chinese exams.

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Tutorial Content

Core Concepts: Solution Concentration and pH Calculations

This section is not only a major area for calculation problems but also the foundation for lab questions (Solution Preparation). In the CSCA exam, the **conversion between Molarity and Mass Percentage** and **pH of Mixtures** are high-frequency topics.

#### 1. Representation and Conversion of Concentration

Besides the basic $c = n/V$, you must master the advanced formula:

* **Core Definition**: $V$ is the volume of the **Solution**, not the solvent!

* **The "Killer" Formula** (Converting Mass Percentage $w$ to Molarity $c$):

$$c = \frac{1000 \cdot \rho \cdot w}{M}$$

* $\rho$: Density of solution (g/cm³ or g/mL)

* $w$: Mass percentage of solute (e.g., 98% or 0.98)

* $M$: Molar mass of solute (g/mol)

* *Logic*: Take 1L (1000 mL) solution $\rightarrow$ Mass $1000\rho$ $\rightarrow$ Solute mass $1000\rho w$ $\rightarrow$ Solute moles $1000\rho w / M$.

#### 2. Preparation of Solutions (Lab Focus)

To prepare a solution of a specific molarity, you must use a **Volumetric Flask**. This is the source of "Error Analysis" questions.

* **Key Steps**: Calculate $\rightarrow$ Weigh $\rightarrow$ Dissolve (Cool) $\rightarrow$ Transfer $\rightarrow$ **Wash** (2-3 times) $\rightarrow$ Fill to Mark (Make up to volume) $\rightarrow$ Shake.

* **Meniscus Error**:

* Reading from above (Parallax error) $\rightarrow$ Water level too low $\rightarrow$ Concentration too high.

* Reading from below $\rightarrow$ Water level too high $\rightarrow$ Concentration too low.

#### 3. Definition and Calculation of pH

* **Definition**: $pH = -\log[H^+]$. Note the **negative logarithm**.

* **Scale**:

#### 4. Advanced Strategies for pH (Mixing Problems)

NEVER add or subtract pH values directly! You must calculate the moles of $H^+$ or $OH^-$ first, mix them to find the new concentration, and then calculate pH.

1. **Acid + Acid**:

$$[H^+]_{mix} = \frac{c_1V_1 + c_2V_2}{V_1 + V_2} \rightarrow \text{Calculate } pH$$

2. **Base + Base**:

**Core**: Calculate $[OH^-]_{mix}$ first!

$$[OH^-]_{mix} = \frac{c(OH^-)_1V_1 + c(OH^-)_2V_2}{V_1 + V_2} \rightarrow \text{Calculate } pOH \rightarrow pH = 14 - pOH$$

3. **Acid + Base (Neutralization)**:

* Determine which is in excess.

* If Acid excess: $[H^+] = (n_{H^+} - n_{OH^-}) / V_{total}$

* If Base excess: $[OH^-] = (n_{OH^-} - n_{H^+}) / V_{total}$

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#### Common Traps and Examples

**Trap 1: pH of Extremely Dilute Acid**

Q: What is the pH of $1.0 \times 10^{-8} \text{ mol/L}$ HCl?

* **Wrong**: pH = 8 (Acid becomes Base? Impossible).

* **Right**: Close to 7 (approx 6.98). Water ionization cannot be ignored when acid is extremely dilute.

**Example: Concentration Conversion**

Commercial concentrated sulfuric acid has density $\rho = 1.84 \text{ g/cm}^3$ and mass percentage $w = 98\%$. Calculate its molarity.

**Solution**:

Use the formula directly:

$$c = \frac{1000 \times 1.84 \times 0.98}{98} = 18.4 \text{ mol/L}$$

**Example: Mixing Bases**

Mix equal volumes of NaOH solution (pH=12) and NaOH solution (pH=10). Calculate the new pH (Given $\log 5 \approx 0.7$).

**Solution**:

1. **Note**: Bases work with $OH^-$.

2. pH=12 $\rightarrow [OH^-]_1 = 10^{-2}$; pH=10 $\rightarrow [OH^-]_2 = 10^{-4}$.

3. Mix: $[OH^-]_{mix} = \frac{10^{-2}V + 10^{-4}V}{2V} \approx \frac{10^{-2}}{2} = 5 \times 10^{-3} \text{ mol/L}$ (Ignore $10^{-4}$).

4. Calc pOH: $pOH = -\log(5 \times 10^{-3}) = 3 - \log 5 = 2.3$.

5. Calc pH: $pH = 14 - 2.3 = 11.7$.