Question

A typical dosage of statin drugs for the treatment of high cholesterol is \(10 \mathrm{mg}\). Assuming a total blood volume of 5.0 L, calculate the \((\mathrm{m} / \mathrm{v}) \%\) concentration of drug in the blood in units of \(\mathrm{g} / 100 \mathrm{~mL}\).

Short answer

The concentration is 0.0002 g/100 mL.

Step-by-step solution

Convert Drug Dosage from mg to g

The given dosage of the statin drug is 10 mg. To work with mass/volume percent, we need the mass in grams. We convert mg to grams by dividing by 1000, since there are 1000 mg in 1 g. So, \[ 10 \text{ mg} = \frac{10}{1000} \text{ g} = 0.01 \text{ g}\].

Calculate Total Volume in mL

The total blood volume given is 5.0 L. We need this volume in milliliters (mL) since the mass/volume percent is calculated per 100 mL. We know that 1 L = 1000 mL, so \[ 5.0 \text{ L} = 5.0 \times 1000 \text{ mL} = 5000 \text{ mL} \].

Calculate the Mass/Volume Percent

The mass/volume percent concentration \((\text{m}/\text{v})\%\) is given by the formula \[ \frac{\text{mass of solute in grams}}{\text{volume of solution in mL}} \times 100 \]. Substituting the values: \[ \frac{0.01 \text{ g}}{5000 \text{ mL}} \times 100 \].

Calculate and Simplify

Now, we compute the fraction and multiply by 100 to find the percentage. \[ \frac{0.01}{5000} \times 100 = \frac{0.01 \times 100}{5000} = \frac{1}{5000} = 0.0002 \]. This result is in \( \text{g} / 100 \text{ mL} \).

Key concepts

Mass/Volume Percent Concentration

When it comes to measuring solutions, chemists use different ways depending on what information is necessary. One commonly used measure is the mass/volume percent concentration.
It expresses the concentration of a solute in a solution as the mass of solute per 100 milliliters of solution. This helps in understanding how much of a substance is present in a given volume, which is particularly useful in medical fields, like pharmaceuticals.

• The formula to calculate the mass/volume percent is: \(\frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}} \times 100\) .
• This calculation shows the percentage of the solution that is composed of the solute, making it easier to compare concentrations.

It's important to ensure that your mass is in grams and your volume is in milliliters before using this formula, as shown in the example previously discussed. By converting the measurement units correctly, you can accurately determine and comprehend the concentration of substances in various mixtures.

Unit Conversion in Chemistry

Unit conversion is a crucial skill in chemistry because it allows us to translate measurements into the units you need for calculation or to report data.
For example, when considering a statin dosage, converting from milligrams to grams or from liters to milliliters is essential to match the units required by a formula or situational context.

• To convert milligrams to grams, divide by 1000, since 1 gram is equivalent to 1000 milligrams.
• Similarly, to convert liters to milliliters, multiply by 1000 because 1 liter is equal to 1000 milliliters.

Conversions like these help standardize data and ensure accuracy, especially when determining concentrations in solutions. Using consistent units is key to avoiding errors during calculations, and it assures that we're speaking the same language through universally understandable terms when sharing results.

Statin Dosage Calculation

Calculating the proper dosage of medications like statins is extremely important in medical chemistry. Statins are drugs prescribed to lower cholesterol levels in the blood, and typically, a precise dose must be administered to ensure efficacy and safety.
In the example exercise, a statin dosage of 10 mg was considered for a total blood volume of 5.0 L.

• The first step is converting milligrams to grams, as calculations for concentration often require mass in grams.
• Next, calculate the total volume in milliliters to pair with the dosage's mass for the mass/volume percent calculation.

Ensuring these conversions are done accurately allows for precise medication dosing. In real-world applications, this is vital for adjusting the concentration to achieve the desired therapeutic effect while minimizing side effects associated with incorrect dosages.