Calculate the mass percentage of aspirin ($C_9H_8O_4$) in acetonitrile ($CH_3CN$) when 6.5 g of $C_9H_8O_4$ is dissolved in 450 g of $CH_3CN$.

Calculate the mass percentage of aspirin (C₉H₈O₄) in acetonitrile (CH₃CN) when 6.5 g of C₉H₈O₄ is dissolved in

Exercises · 1.28

C_9H_8O_4

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Concept understanding — Mass Percentage

Mass Percentage: The Intuition

Imagine you're making lemonade. You mix 50 grams of sugar into 200 grams of water. The total drink weighs 250 grams. Now, if someone asks, "How much of this drink is actually sugar?" — you're not just saying "50 grams." You want to say what fraction of the whole mixture is sugar, scaled to a convenient 100.

That's mass percentage. It answers: "Out of every 100 grams of the mixture, how many grams are this particular component?"

In our lemonade, sugar is 50 g out of 250 g total. That's $\frac{50}{250} = 0.2$ of the whole. Multiply by 100 to get the percentage: $0.2 \times 100 = 20\%$ . So, 20% of the drink's mass is sugar. If you had 100 g of this lemonade, 20 g of it would be sugar.

The Precise Definition

\text{Mass percentage of component} = \frac{\text{Mass of that component}}{\text{Total mass of mixture}} \times 100\%

The formula is simple, but the key is understanding what "total mass" means. It's the sum of masses of all components in the mixture — nothing more, nothing less.

Why It Matters in Chemistry

Mass percentage is one of the most common ways to express concentration — how much of a substance is present in a mixture. You'll see it in:

Solutions: "10% salt water" means 10 g of salt dissolved in enough water to make 100 g of solution (not 10 g salt + 100 g water — that would be 110 g total, giving only about 9.1%).
Alloys: "18-karat gold" is 75% gold by mass (18 parts gold out of 24 total parts).
Food labels: "Fat: 15%" means 15 g of fat per 100 g of the food.

Watch out

A Common Mistake

Students often think "10% salt solution" means 10 g salt + 100 g water. That's wrong. It means 10 g salt + 90 g water = 100 g total solution. The denominator is total mass, not the mass of the solvent alone.

Step-by-Step Example

Problem: A solution is made by dissolving 25 g of glucose in 175 g of water. Find the mass percentage of glucose.

Step 1: Identify the component you care about — glucose (25 g).

Step 2: Find the total mass of the mixture.

\text{Total mass} = 25\ \text{g (glucose)} + 175\ \text{g (water)} = 200\ \text{g}

Step 3: Apply the formula.

$\text{Mass percentage of glucose} = \frac{25}{200} \times 100\% = 12.5\%$ …

Why this formula?

Let's break down Mass Percentage from first principles. The goal is to understand why the formula is what it is, not just to memorize it.

1. The Core Idea: "Part of a Whole"

Mass percentage answers a simple question: "If I break a mixture into 100 equal parts by mass, how many of those parts come from a specific component?"

Imagine you have a bowl of fruit salad. The total mass is 500 grams. The apples in it weigh 100 grams.

The apples are a part of the whole salad.
The whole salad is the total.

The mass percentage tells you the fraction of the total mass that is apples, but expressed "out of 100" (per cent).

2. The Natural First Step: The Fraction

Before we talk about "percentage," we talk about the fraction of the total:

\text{Fraction of component} = \frac{\text{Mass of component}}{\text{Total mass of mixture}}

For the apple example:

\frac{100 \text{ g}}{500 \text{ g}} = 0.2

This means 0.2 (or one-fifth) of the total mass is apples. This is the pure ratio — no scaling yet.

3. Why Multiply by 100?

A fraction like 0.2 is perfectly correct, but it's not intuitive for quick comparison. "Per cent" literally means "per hundred" (from Latin per centum).

To convert a fraction into a "per hundred" number, we multiply by 100:

\text{Percentage} = (\text{Fraction}) \times 100

So:

0.2 \times 100 = 20\%

This tells us: "Out of every 100 grams of fruit salad, 20 grams come from apples." That's much easier to visualize.

4. The Final Formula (The "Why" in One Line)

Putting the fraction and the "times 100" together gives the standard formula:

\text{Mass percentage} = \frac{\text{Mass of component}}{\text{Total mass of mixture}} \times 100\%

Why does this work?

Because it's just:

Find the proportion (part ÷ whole).
Scale that proportion to per hundred (× 100).

5. A Common Exam Trap (and Why It's Wrong)

Sometimes students write: …

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The mass percentage of a component in a solution is the ratio of its mass to the total mass of the solution, expressed as a percentage. For this problem, the mass percentage of aspirin is calculated as $\frac{\text{mass of aspirin}}{\text{mass of aspirin} + \text{mass of acetonitrile}} \times 100\%$ , which results in $\boxed{1.42\%}$ .

When we talk about the concentration of a solution, we're describing how much solute is dissolved in a given amount of solvent or solution. There are many ways to express concentration, and one of the most fundamental is mass percentage.

Mass percentage, also known as mass/mass percentage or percent by mass, tells us the mass of a particular component (usually the solute) present in 100 units of mass of the total solution. It's a very practical unit because mass is an additive property and doesn't change with temperature or pressure, unlike volume. This makes mass percentage a reliable way to express concentration in many chemical and industrial applications.

The core idea is to find the fraction of the total mass that belongs to the component of interest and then multiply by 100 to express it as a percentage.

Here's how we calculate it for aspirin in acetonitrile:

Identify the Solute and Solvent

In this problem, aspirin ( $C_9H_8O_4$ ) is the substance being dissolved, making it the solute. Acetonitrile ( $CH_3CN$ ) is the substance doing the dissolving, making it the solvent.
List the Given Masses

We are given:
- Mass of aspirin (solute) $= 6.5 \text{ g}$
- Mass of acetonitrile (solvent) $= 450 \text{ g}$
Calculate the Total Mass of the Solution

A solution is formed when a solute dissolves in a solvent. The total mass of the solution is simply the sum of the mass of the solute and the mass of the solvent.

Total mass of solution $=$ Mass of solute $+$ Mass of solvent

Total mass of solution $= 6.5 \text{ g} + 450 \text{ g}$

Total mass of solution $= 456.5 \text{ g}$ …

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Here are the common mistakes students make when solving this Mass Percentage problem, and how to avoid each.

1. Using the wrong formula for mass percentage

Mistake:

Students often confuse mass percentage with mole fraction or volume percentage. They might divide the mass of solute by the mass of solvent only, or use total moles instead of total mass.

How to avoid:

Always recall the definition:

\text{Mass \%} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100

The solution = solute + solvent.

Here:

Solute = aspirin = $6.5 \, \text{g}$
Solvent = acetonitrile = $450 \, \text{g}$
Solution mass = $6.5 + 450 = 456.5 \, \text{g}$

So:

\text{Mass \%} = \frac{6.5}{456.5} \times 100 \approx 1.42\%

Key point: Denominator is solution mass, not solvent mass.

2. Forgetting to add solute and solvent masses

Mistake:

Using only $450 \, \text{g}$ in the denominator.

Why it happens:

Students think “mass percentage” means “mass of solute per 100 g of solvent” — that’s actually molality or a ratio, not mass percentage.

How to avoid:

Write down:

\text{Total mass} = m_{\text{solute}} + m_{\text{solvent}}

Then plug into the formula. Never skip this step.

3. Incorrect molar mass calculations (unnecessary here)

Mistake:

Students calculate molar masses of aspirin ( $C_9H_8O_4$ ) and acetonitrile ( $CH_3CN$ ) and try to use moles — even though the question only asks for mass percentage, which uses grams directly.

How to avoid:

Read the question carefully. If it asks for mass percentage, you only need masses in grams. Molar masses are irrelevant unless the question asks for mole fraction or molality.

Exam tip: Mass percentage is a mass-only concept. No moles needed.

4. Rounding too early

Mistake: …

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Q.Calculate the mass percentage of aspirin ( $C_9H_8O_4$ ) in acetonitrile ( $CH_3CN$ ) when 6.5 g of $C_9H_8O_4$ is dissolved in 450 g of $CH_3CN$ .

Concept understanding — Mass Percentage

Mass Percentage: The Intuition

The Precise Definition

Why It Matters in Chemistry

Step-by-Step Example

Why this formula?

1. The Core Idea: "Part of a Whole"

2. The Natural First Step: The Fraction

3. Why Multiply by 100?

4. The Final Formula (The "Why" in One Line)

5. A Common Exam Trap (and Why It's Wrong)

Method: Mass Percentage (or Weight/Weight Percentage)

Concept (Why this works)

Steps

1. Using the wrong formula for mass percentage

2. Forgetting to add solute and solvent masses

3. Incorrect molar mass calculations (unnecessary here)

4. Rounding too early

Q.Calculate the mass percentage of aspirin (C9H8O4C_9H_8O_4C9​H8​O4​) in acetonitrile (CH3CNCH_3CNCH3​CN) when 6.5 g of C9H8O4C_9H_8O_4C9​H8​O4​ is dissolved in 450 g of CH3CNCH_3CNCH3​CN.

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Q.Calculate the mass percentage of aspirin ( $C_9H_8O_4$ ) in acetonitrile ( $CH_3CN$ ) when 6.5 g of $C_9H_8O_4$ is dissolved in 450 g of $CH_3CN$ .

Unlock everything free for 14 days