Expressing the Concentration of Solutions 🧪

When you mix a substance (the solute) with another substance (the solvent) you get a solution. Saying a drink is “very sweet” or “a bit salty” is vague, so chemists rely on numbers to describe how much solute sits in a given amount of solvent or solution. Let’s tour the seven most useful ways to do this!

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1. Mass Percentage (w/w) 🏋️‍♂️

$$\text{Mass \% of a component}= \frac{\text{Mass of the component in the solution}}{\text{Total mass of the solution}}\times100$$ :contentReference[oaicite:0]{index=0}

• 10 % glucose in water means 10 g glucose + 90 g water → 100 g solution.
• Industry loves this unit—for example, household bleach holds ≈ 3.62 % sodium hypochlorite.

2. Volume Percentage (v/v) 🧴

$$\text{Volume \% of a component}= \frac{\text{Volume of the component}}{\text{Total volume of the solution}}\times100$$ :contentReference[oaicite:1]{index=1}

• 10 % (v/v) ethanol in water ⇒ 10 mL ethanol + water up to 100 mL.
• Cars use 35 % (v/v) ethylene glycol as antifreeze—it stops water from freezing at –17.6 °C.

3. Mass-by-Volume Percentage (w/v) 💊

Mass of solute in 100 mL of solution (common in medicine and pharmacy). :contentReference[oaicite:2]{index=2}

4. Parts Per Million (ppm) 🌊

$$\text{ppm}= \frac{\text{Number of parts of the component}}{\text{Total parts of all components}}\times10^{6}$$ :contentReference[oaicite:3]{index=3}

• Sea water carries about 5.8 ppm dissolved oxygen.
• Great for pollutant levels in water or air.

5. Mole Fraction (x) ⚖️

$$x_i=\frac{n_i}{\sum n_i}\quad\text{and}\quad\sum x_i = 1$$ :contentReference[oaicite:4]{index=4}

• For a binary mix: $$x_A=\frac{n_A}{n_A+n_B}$$
• Ideal when you need to link concentration to properties like vapour pressure.

6. Molarity (M) 🧪

$$M=\frac{\text{Moles of solute}}{\text{Volume of solution in L}}$$ :contentReference[oaicite:5]{index=5}

• 0.25 M NaOH ⇒ 0.25 mol NaOH in exactly 1 L solution.
• Temperature-dependent because volume changes with heat.

7. Molality (m) 🏋️‍♀️

$$m=\frac{\text{Moles of solute}}{\text{Mass of solvent in kg}}$$ :contentReference[oaicite:6]{index=6}

• 1.00 m KCl means 1 mol KCl per 1 kg water.
• Temperature-independent (mass stays put when things heat up).

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Temperature Tip 🔥❄️

Mass %, ppm, mole fraction, and molality shrug off temperature changes, while molarity feels the heat because volume can expand or contract. :contentReference[oaicite:7]{index=7}

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Quick Worked Examples 📚

• Mole fraction of ethylene glycol in a 20 % (w/w) solution: $$x_{\text{glycol}}=0.068$$, $$x_{\text{water}}=0.932$$ :contentReference[oaicite:8]{index=8}
• Molarity of 5 g NaOH in 450 mL solution: $$M=0.278$$ mol L⁻¹ :contentReference[oaicite:9]{index=9}
• Molality of 2.5 g CH₃COOH in 75 g benzene: $$m=0.556$$ mol kg⁻¹ :contentReference[oaicite:10]{index=10}

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Try These Yourself 📝

1. Find the mass % of benzene if 22 g C₆H₆ dissolves in 122 g CCl₄.
2. 30 % (w/w) benzene in CCl₄ → what’s the mole fraction of benzene?
3. Compute molarity for:
   • (a) 30 g Co(NO₃)₂·6H₂O in 4.3 L,
   • (b) 30 mL of 0.5 M H₂SO₄ diluted to 500 mL.
4. How much urea makes 2.5 kg of 0.25 m aqueous solution?
5. For 20 % (w/w) KI (density 1.202 g mL⁻¹), find (a) molality, (b) molarity, (c) mole fraction.

:contentReference[oaicite:11]{index=11}

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High-Yield NEET Takeaways 🎯

• 🔢 Memorize the seven key formulas—they appear often.
• 🌡️ Know which units do and don’t depend on temperature.
• 🔁 Be ready to convert between molarity, molality, and mole fraction.
• 🚰 ppm pops up in environmental chemistry questions (water/air pollutants).
• 🧩 Mole fraction quickly links concentration to properties like vapour pressure—handy for colligative property problems.

Happy studying—keep practicing and those equations will feel like second nature! 😊