A drinking water sample contains mass concentration in mg/L? Assume 1 kg (1000 g) solution. 1 = x / (1000 * a) × 10^6
Understand the Problem
The question is asking how to calculate the mass concentration of a drinking water sample in mg/L, using the provided formula which relates mass and concentration.
Answer
$$ x = \frac{1000 \cdot a}{10^6} $$
Answer for screen readers
The mass concentration of the drinking water sample is given by the formula:
$$ x = \frac{1000 \cdot a}{10^6} $$
This means that if $a$ is known, you can directly calculate the concentration in mg/L.
Steps to Solve
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Understanding the Equation
Given the equation:
$$ 1 = \frac{x}{1000 \cdot a} \times 10^6 $$
This equation relates the concentration ($x$) to $a$, where $a$ is the factor you need to determine for your specific solution.
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Rearranging the Equation
To isolate $x$, you can first rearrange the equation:
$$ x = 1 \cdot (1000 \cdot a) \div 10^6 $$
Simplifying this gives us:
$$ x = \frac{1000 \cdot a}{10^6} $$
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Simplifying the Expression
Now, you can simplify further:
$$ x = \frac{1000}{10^6} \cdot a $$
This simplifies to:
$$ x = \frac{1}{1000} \cdot a $$
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Calculating Mass Concentration
Suppose you have a specific value for $a$. You can substitute it into this simplified equation to find the mass concentration in mg/L:
$$ \text{Concentration in mg/L} = \frac{a}{1000} $$
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Finalizing the Calculation
For example, if $a$ were to be given as 300, you would substitute it into the equation:
$$ x = \frac{300}{1000} = 0.3 \text{ mg/L} $$
The mass concentration of the drinking water sample is given by the formula:
$$ x = \frac{1000 \cdot a}{10^6} $$
This means that if $a$ is known, you can directly calculate the concentration in mg/L.
More Information
Mass concentration in dilute solutions is usually measured in mg/L, which helps in assessing the quality of water.
Tips
- Forgetting to convert the units when dealing with mass and volume.
- Not correctly rearranging the equation to isolate the variable of interest ($x$).
