Question

How many ${\text{g/mL}}$ are in $12{\text{ cg/L}}$?

Answer 1

${\text{g/mL}}$ and ${\text{cg/L}}$ are the units of measurement of concentrations. To solve this we must know the relationship between gran and centigram. Also, we must know the relationship between millilitre and litre. From these relationships convert $12{\text{ cg/L}}$ to ${\text{g/mL}}$.

Complete solution:
We must know the relationship between gran and centigram. Also, we must know the relationship between millilitre and litre. ${\text{g/mL}}$ and ${\text{cg/L}}$ are the units of measurement of concentrations.
Now, we know that one gram is equal to a hundred centigram. Thus,
${\text{1 g}} = {\text{100 cg}}$
And,
${\text{1 cg}} = {\text{1}}{{\text{0}}^{ - 2}}{\text{ g}}$
We know that one litre is equal to a thousand millilitre. Thus,
${\text{1 L}} = {\text{1000 mL}}$
And,
${\text{1 mL}} = {\text{1}}{{\text{0}}^{ - 3}}{\text{ L}}$
We are given that the concentration is $12{\text{ cg/L}}$.
Let us convert $12{\text{ cg}}$ to grams using the relation as follows:
${\text{1 cg}} = {\text{1}}{{\text{0}}^{ - 2}}{\text{ g}}$
Thus,
$12{\text{ cg}} = 12{\text{ cg}} \times \dfrac{{{{10}^{ - 2}}{\text{ g}}}}{{1{\text{ cg}}}} = 0.12{\text{ g}}$
Thus, $12{\text{ cg}}$ is equal to $0.12{\text{ g}}$.
$12{\text{ cg/L}}$ suggests that there are 12 centigram in one litre. Or there are 0.12 gram in 1000 millilitres.
Now, we have 0.12 gram in 1000 millilitres. Calculate the amount in 1 millilitre as follows:
$1{\text{ mL}} = 1{\text{ mL}} \times \dfrac{{0.12{\text{ g}}}}{{1000{\text{ mL}}}} = 0.00012{\text{ g}}$
Thus, there is $0.00012{\text{ g}}$ in one millilitre.
Thus, $12{\text{ cg/L}}$ is equal to $0.00012{\text{ g/mL}}$.

Note: Another method to solve this is as follows: We know that one gram is equal to $100 \times {\text{cg}}$ and one litre is equal to $1000 \times {\text{mL}}$. Thus, divide 12 by $100 \times 1000 = 100000$. Thus,
$12{\text{ cg/L}} = \dfrac{{12}}{{100000}}{\text{g/mL}} = 0.00012{\text{ g/mL}}$