Convert 8.2 mg/dL calcium to millimoles per liter (mmol/L). The gmw of calcium is 40 g. So, if there are 40 g per mol, then it follows that there are 40 mg per mmol. The final units wanted are mmol/L. The equation becomes
Once again, the systematic stepwise approach of deleting similar units can be used for this conversion problem. A frequently encountered conversion problem or, more precisely, a dilution problem occurs when a weaker concentration or different volume is needed than the stock substance available, but the concentration terms are the same. The following formula is used where V1 is the volume of the first substance, C1 is the concentration of the first substance, V2 is the volume of the second substance, and C2 is the concentration of the second substance:
(Eq. 1-38)
This formula is useful only if the concentration and volume units between the substances are the same and if three of four variables are known.
The correct answer and explanation is:
Answer:
To convert 8.2 mg/dL calcium to mmol/L, we use the given information:
- The gram molecular weight (gmw) of calcium is 40 g/mol.
- This means 1 mmol of calcium = 40 mg.
Now, apply unit conversion:
[
\frac{8.2 \text{ mg}}{1 \text{ dL}} \times \frac{1 \text{ dL}}{0.1 \text{ L}} \times \frac{1 \text{ mmol}}{40 \text{ mg}}
]
Breaking it down:
- Convert mg to mmol using the given molecular weight: [
\frac{8.2 \text{ mg}}{40 \text{ mg/mmol}} = 0.205 \text{ mmol}
] - Convert dL to L (1 dL = 0.1 L): [
\frac{0.205 \text{ mmol}}{0.1 \text{ L}} = 2.05 \text{ mmol/L}
]
Final Answer:
[
8.2 \text{ mg/dL} = 2.05 \text{ mmol/L}
]
Explanation:
Understanding unit conversions is crucial in medical, pharmaceutical, and laboratory sciences. This specific calculation is often used in clinical settings to assess calcium levels in the blood. Calcium plays a vital role in nerve function, muscle contraction, and bone health, making its accurate measurement essential.
The conversion follows a systematic approach, eliminating units step by step:
- Convert mg to mmol: Since 1 mmol of calcium weighs 40 mg, dividing the given mg value by 40 converts it into mmol.
- Convert dL to L: Since 1 dL = 0.1 L, we divide by 0.1 to get the concentration in mmol/L, which is the standard SI unit used in medical and laboratory reports.
This stepwise elimination of similar units ensures accuracy. It’s also important in dilution problems, where maintaining consistent units helps avoid calculation errors.
For example, when adjusting the concentration of a solution, the dilution formula:
[
C_1V_1 = C_2V_2
]
ensures that the new concentration and volume are correctly balanced. This principle applies in IV drug preparation, reagent mixing, and various medical calculations.
Now, I’ll generate an image illustrating the conversion process.
I’ve provided an image illustrating the step-by-step conversion of calcium concentration from 8.2 mg/dL to mmol/L, following the outlined method. Let me know if you need any modifications or further explanations!
