Question

ketamine, sometimes used as an adjuvant to general anesthesia, is available as a 10.0 %(w/v) solution. calculate the mass of ketamine in 1.00 ml of this solution. be sure your answer has a unit symbol and is rounded to the correct number of significant digits.

Explanation:

Step1: Understand the formula for mass - by - volume percentage

The formula for mass - by - volume percentage (\(w/v\)) is \(\text{Mass - by - volume}\%=\frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}}\times100\). We can re - arrange this formula to solve for the mass of the solute. Let \(m\) be the mass of ketamine (solute), \(V\) be the volume of the solution (\(V = 1.00\space mL\)), and the mass - by - volume percentage \(=10.0\%\). From \(\text{Mass - by - volume}\%=\frac{m}{V}\times100\), we can solve for \(m\) as \(m=\frac{\text{Mass - by - volume}\%\times V}{100}\).

Step2: Substitute the values into the formula

Substitute \(\text{Mass - by - volume}\% = 10.0\) and \(V=1.00\space mL\) into the formula \(m=\frac{10.0\times1.00}{100}\).

$$m=\frac{10.0\times1.00}{100}=0.100\space g$$

Answer:

\(0.100\space g\)