10.30 mg of O2 is dissolved into a litre of sea water of density 1.03 g/mL. The concentration of O2

Q: Why do we multiply by $10^6$ in the ppm formula?

"ppm" stands for "parts per million". Just like percentage (%) multiplies by 100 to find parts per hundred, ppm multiplies by $1,000,000$ ($10^6$) to find how many parts of solute exist in one million parts of the total solution.

Q: Can I use the volume of the solution directly instead of its mass?

For very dilute aqueous solutions where the density is exactly $1 \text{ g/mL}$, $1 \text{ L}$ of solution weighs exactly $1 \text{ kg}$, so you can sometimes use $\text{mg/L}$ as a shortcut for ppm. However, here the density is $1.03 \text{ g/mL}$, so you *must* calculate the exact mass to avoid errors.

Q: Why did we convert $1 \text{ L}$ to $1000 \text{ mL}$?

The density of the sea water is given in $\text{g/mL}$. To cancel out the volume units and get the mass in grams, the volume must also be in $\text{mL}$.

Q: Does the mass of the solution include the mass of the oxygen?

Technically, yes. The total mass of the solution is the mass of the solvent plus the mass of the solute. However, $10.30 \text{ mg}$ ($0.0103 \text{ g}$) is so incredibly small compared to $1030 \text{ g}$ of sea water that adding it ($1030.0103 \text{ g}$) doesn't change the final answer within significant figures.

Q: What if the solute mass was given in micrograms ($\mu\text{g}$)?

You would follow the exact same logic, but you would convert micrograms to grams by multiplying by $10^{-6}$ instead of $10^{-3}$. Consistency in units is the key!

Question

10.30 mg of $O_2$ is dissolved into a litre of sea water of density 1.03 g/mL. The concentration of $O_2$ in ppm is

Sigma Percentile · Accepted Answer

### Analyzing the Setup
Imagine you are standing by the ocean, holding a beaker filled with exactly one litre of sea water. Within this vast volume of water, a minuscule amount of oxygen gas—just $10.30 	ext{ mg}$—is dissolved. This dissolved oxygen is what sustains marine life! Our mission is to express this tiny concentration in a more intuitive unit: parts per million (ppm).

To do this, we need to compare the mass of the oxygen to the total mass of the sea water. But right now, we have the volume of the water and the mass of the oxygen in different units. We need to bring everything onto a level playing field.

### The Master Equation
The formula for parts per million is beautifully simple. It tells us how many parts of solute exist in one million parts of the solution.

$$ 	ext{ppm} = \frac{	ext{Mass of solute}}{	ext{Mass of solution}} 	imes 10^6 $$

**Crucial Step:** Both masses must be in the exact same unit, typically grams, before we can plug them into this equation. Don't make the silly mistake of mixing milligrams and kilograms!

### Finding the Mass of the Solution
We are given the volume of the sea water as $1 	ext{ L}$, which is equivalent to $1000 	ext{ mL}$. We are also given its density, $d = 1.03 	ext{ g/mL}$.

Using the fundamental relationship between mass, volume, and density, we can find the total mass of our solution:

$$ m_{	ext{solution}} = V 	imes d $$

$$ m_{	ext{solution}} = 1000 	ext{ mL} 	imes 1.03 	ext{ g/mL} $$

$$ m_{	ext{solution}} = 1030 	ext{ g} $$

### Converting the Solute Mass
Now, let's look at our solute, the oxygen gas. Its mass is given as $10.30 	ext{ mg}$. To convert milligrams to grams, we multiply by $10^{-3}$.

$$ m_{	ext{solute}} = 10.30 	imes 10^{-3} 	ext{ g} $$

### Final Calculation
We have our raw ingredients ready. Let's substitute them into the master equation:

$$ 	ext{ppm} = \frac{10.30 	imes 10^{-3} 	ext{ g}}{1030 	ext{ g}} 	imes 10^6 $$

Let's simplify the powers of ten first. Multiplying $10^{-3}$ by $10^6$ gives us $10^3$, or $1000$.

$$ 	ext{ppm} = \frac{10.30 	imes 1000}{1030} $$

$$ 	ext{ppm} = \frac{10300}{1030} $$

Dividing these numbers gives us a clean, perfect integer:

$$ 	ext{ppm} = 10 $$

The concentration of dissolved oxygen in the sea water is exactly **10 ppm**. This means for every one million grams of sea water, there are 10 grams of oxygen dissolved in it!

Animated Solution for Chemistry - Basic Concepts in Chemistry: 10.30 mg of $O_{2}$ is dissolved into a litre of sea water of density 1.03 g/mL. The concentration of $O_{2}$ in ppm is

Enter Numerical Value:

Visualized Solution

$Visualizing the Setup$

$Formula for ppm$

$Mass of Solution$

$Mass of Solute in Grams$

$Substituting Values$

$Simplifying the Expression$

$Final Calculation$

$Conclusion & Extensions$

The Sigma Insight: Molecular Mass, Mole Concept and Concentration

Analyzing the Setup Imagine you are standing by the ocean, holding a beaker filled with exactly one litre of sea water

The Master Equation The formula for parts per million is beautifully simple

Finding the Mass of the Solution We are given the volume of the sea water as $1 L$ , which is equivalent to $1000 mL$

Converting the Solute Mass Now, let's look at our solute, the oxygen gas

Final Calculation We have our raw ingredients ready

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Enter Numerical Value:

Visualized Solution

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Visualizing the Setup

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Formula for ppm

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Mass of Solution

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Mass of Solute in Grams

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Substituting Values

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Simplifying the Expression

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Final Calculation

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Conclusion & Extensions