To convert nmol/L to ng/dL for testosterone:
Step 1: Convert nmol/L to mol/L
\[ \text{mol/L} = \text{nmol/L} \times 10^{-9} \]
Step 2: Convert mol/L to g/L using molar mass
\[ \text{g/L} = \text{mol/L} \times \text{molar mass} \]
Step 3: Convert g/L to ng/L
\[ \text{ng/L} = \text{g/L} \times 10^9 \]
Step 4: Convert ng/L to ng/dL
\[ \text{ng/dL} = \frac{\text{ng/L}}{10} \]
Conversion of concentration units involves using the molecular weight of the substance. In this example, we convert nmol/L to ng/dL for testosterone, which has a molecular weight of 288.42 g/mol.
Assume the value is 10 nmol/L.
Step 1: Convert nmol/L to mol/L:
\[ 10 \times 10^{-9} = 10 \times 10^{-9} \, \text{mol/L} \]
Step 2: Convert mol/L to g/L:
\[ 10 \times 10^{-9} \, \text{mol/L} \times 288.42 \, \text{g/mol} = 2.8842 \times 10^{-6} \, \text{g/L} \]
Step 3: Convert g/L to ng/L:
\[ 2.8842 \times 10^{-6} \, \text{g/L} \times 10^9 = 2884.2 \, \text{ng/L} \]
Step 4: Convert ng/L to ng/dL:
\[ \frac{2884.2}{10} = 288.42 \, \text{ng/dL} \]
So, 10 nmol/L is approximately 288.42 ng/dL.