Question

A form of children's Tylenol is sold as a suspension (in which the drug is suspended in water) that contains \(32 \mathrm{mg} /\) \(\mathrm{mL}\). Convert this concentration into each alternative unit. (a) \(g / L\) (b) \(g / d L\) (c) \(\mathrm{kg} / \mathrm{hL}\) (d) \(\mu g / \mu \mathrm{L}\)

Short answer

a) 32 g/L, b) 320 g/dL, c) 3.2 kg/hL, d) 32 \(\mu g / \mu L\)

Step-by-step solution

Understand the Conversion for Part (a)

Convert the given concentration from mg/mL to g/L. Since 1 mg is equal to 0.001 g and 1 mL is equal to 0.001 L, we can convert 32 mg/mL to g/L by multiplying by the conversion factors.

Calculate the Conversion for Part (a)

To get the concentration in g/L, multiply 32 mg/mL by the factor 0.001 g/mg, and since mL and L are in the same unit family, 1 mL is 0.001 L resulting in the original volume in L, thus: \[ 32 \frac{mg}{mL} * 0.001 \frac{g}{mg} * 1 \frac{mL}{0.001 L} = 32 \frac{g}{L} \]

Understand the Conversion for Part (b)

Now, convert the given concentration to g/dL. Knowing that 1 L is equal to 10 dL, we will use this conversion to change our units.

Calculate the Conversion for Part (b)

To get the concentration in g/dL, multiply 32 g/L by (10 dL/1 L): \[ 32 \frac{g}{L} * \frac{10 dL}{1 L} = 320 \frac{g}{dL} \]

Understand the Conversion for Part (c)

To convert the concentration to kg/hL, we'll use the fact that 1 g is equal to 0.001 kg and 1 hL is 100 L.

Calculate the Conversion for Part (c)

To find the concentration in kg/hL, first convert g to kg by multiplying by 0.001, and then convert L to hL by multiplying by 0.01: \[ 32 \frac{g}{L} * 0.001 \frac{kg}{g} * \frac{1 L}{0.01 hL} = 3.2 \frac{kg}{hL} \]

Understand the Conversion for Part (d)

We need to transform the units from mg/mL to \(\mu g / \mu L\). Remember that 1 mg is equivalent to 1000 \(\mu g\) and 1 mL is equivalent to 1000 \(\mu L\).

Calculate the Conversion for Part (d)

Multiply 32 mg/mL by the conversion factors to obtain the concentration in \(\mu g / \mu L\): \[ 32 \frac{mg}{mL} * \frac{1000 \mu g}{1 mg} * \frac{1 mL}{1000 \mu L} = 32 \frac{\mu g}{\mu L} \]

Key concepts

Chemistry Calculations

Chemistry calculations, such as those involving concentration conversions, require meticulous attention to detail and an understanding of the mole concept, molarity, and molality, among others. Accurate calculations are necessary for preparing solutions, performing titrations, and calculating yields.

In our example involving the Tylenol suspension, calculating the different units of concentration involves straightforward arithmetic once the conversion factors are known. It's essential to maintain the integrity of your units throughout the calculation process, which is why dimensional analysis is so valuable. It provides a structured method to ensure the final result is in the correct units, be it g/L, g/dL, kg/hL, or \begin{math}\begin{math}\begin{math}\begin{math}\begin{math}mu g / mu L\begin{math}\begin: \begin{math}\begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \begin: \reiben: \begin: \rootScope.xx = {}; \rootScope.xx.texButtonCb = function() { MathJax.Hub.Queue(function() { $$ .each( $$('script[type=