To make 2 liters of 0.4 M HCl, how many ml of 28% w/w HCl (specific gravity = 1.15) is required?
(1) 80.7
(2) 90.7
(3) 100.7
(4) 110.7
How to Make 0.4 M HCl from 28% w/w Concentrated Solution – Step-by-Step Calculation
Making accurate dilutions from concentrated acids is a common task in labs, especially when working with hydrochloric acid (HCl). In this article, we’ll calculate how many milliliters of 28% w/w HCl (with specific gravity 1.15) are needed to prepare 2 liters of 0.4 M HCl.
🧪 Given Data
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Desired volume: 2 liters (2000 mL)
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Desired molarity: 0.4 M
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Concentrated HCl: 28% w/w
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Specific gravity: 1.15
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Molar mass of HCl: 36.5 g/mol
🔍 Step-by-Step Solution
Step 1: Convert % w/w to Molarity
To find how many grams of HCl are in 1 liter of concentrated acid:
\text{28% w/w} \Rightarrow 28 \, \text{g HCl in 100 g solution}
Specific gravity = 1.15 means:
1000 mL of solution weighs=1000×1.15=1150 g\text{1000 mL of solution weighs} = 1000 \times 1.15 = 1150 \, \text{g} So, amount of HCl in 1 liter=28100×1150=322 g HCl\text{So, amount of HCl in 1 liter} = \frac{28}{100} \times 1150 = 322 \, \text{g HCl}
Now convert grams to moles:
Moles of HCl=32236.5≈8.82 mol\text{Moles of HCl} = \frac{322}{36.5} \approx 8.82 \, \text{mol}
So, molarity of stock solution = 8.82 M
Step 2: Use Dilution Formula
M1V1=M2V2M_1V_1 = M_2V_2
Where:
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M1=8.82 MM_1 = 8.82 \, \text{M}
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V1=V_1 = volume of stock solution needed (what we want)
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M2=0.4 MM_2 = 0.4 \, \text{M}
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V2=2000 mLV_2 = 2000 \, \text{mL}
V1=M2×V2M1=0.4×20008.82≈90.7 mLV_1 = \frac{M_2 \times V_2}{M_1} = \frac{0.4 \times 2000}{8.82} \approx 90.7 \, \text{mL}
✅ Correct Answer: (2) 90.7 mL
💡 Summary Table
| Parameter | Value |
|---|---|
| Desired volume | 2 liters (2000 mL) |
| Desired molarity | 0.4 M |
| HCl stock concentration | 28% w/w |
| Specific gravity | 1.15 |
| Molar mass of HCl | 36.5 g/mol |
| Volume required from stock | 90.7 mL |
Why This Is Important
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Inaccurate acid dilutions can lead to failed experiments or dangerous conditions.
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Understanding these calculations helps in chemical preparation, buffer design, and standard solution formulation.
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It’s a critical skill for chemists, biologists, pharmacists, and students in lab settings.
Final Thoughts
If you’re ever asked “How much 28% w/w HCl do I need to prepare 2 L of 0.4 M HCl?”, you now know that the answer is 90.7 mL. Use the dilution formula wisely, understand the physical properties of your chemicals (like specific gravity), and always double-check your unit conversions.
Mastering these skills ensures safe and accurate chemical preparation every time!
