Convert 400 nmol/mL to µM (Micromolar). Show your calculations.
The correct answer and explanation is :
To convert 400 nmol/mL to µM (micromolar), we need to understand the relationship between the units involved.
Step-by-Step Calculation
We start with:
$$
400\ \text{nmol/mL}
$$
We want to convert this to:
$$
\mu M = \mu mol/L
$$
Step 1: Convert nanomoles (nmol) to micromoles (µmol)
$$
1\ \mu mol = 1,000\ nmol
\Rightarrow 400\ \text{nmol} = \frac{400}{1000} = 0.4\ \mu mol
$$
Step 2: Convert mL to L
$$
1\ L = 1,000\ mL
\Rightarrow 1\ mL = \frac{1}{1000}\ L
$$
So, if you have 0.4 µmol in 1 mL, then in 1 liter (L), you would have:
$$
0.4\ \mu mol/mL \times 1000\ mL = 400\ \mu mol/L = 400\ \mu M
$$
✅ Final Answer: 400 µM
300-Word Explanation
To convert from nmol/mL to µM (micromolar), it’s important to understand the metric prefixes and how they relate to concentration units.
Nanomoles (nmol) and micromoles (µmol) are both units of amount of substance in the metric system, with nano- meaning $10^{-9}$ and micro- meaning $10^{-6}$. Thus, one micromole is equal to 1,000 nanomoles:
$$
1\ \mu mol = 1000\ nmol
$$
Micromolar (µM) is a unit of concentration that refers to micromoles per liter (µmol/L). Since our original unit is nmol/mL, we need to convert both the numerator (nmol) and the denominator (mL) into µmol and liters, respectively.
We first convert the 400 nmol to micromoles:
$$
400\ nmol = 400 \div 1000 = 0.4\ \mu mol
$$
Then we recognize that 1 mL equals $1/1000$ of a liter. So having 0.4 µmol in 1 mL means:
$$
0.4\ \mu mol/mL \times 1000\ mL = 400\ \mu mol/L
$$
And since µmol/L = µM, the final concentration is:
$$
\boxed{400\ \mu M}
$$
This demonstrates that a concentration of 400 nmol/mL is numerically equal to 400 µM. Understanding these conversions is critical in biology, pharmacology, and clinical chemistry, where precise measurements of chemical concentrations are necessary for dosing, reactions, and lab testing.