Question

normal saline, a 0.90 %(w/v) solution of salt (nacl)in water, is often used as an iv carrier fluid in hospitals. calculate the mass of nacl in 145. 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 \((w/v)\) percentage

The formula for \((w/v)\) (weight - by - volume percentage) is \(\%(w/v)=\frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}}\times100\). We can rearrange this formula to solve for the mass of the solute. Let \(m\) be the mass of \(NaCl\) (solute) and \(V\) be the volume of the solution. Then \(m=\frac{\%(w/v)\times V}{100}\).

Step2: Substitute the given values into the formula

We are given that \(\%(w/v) = 0.90\%\) and \(V=145\space mL\). Substituting these values into the formula \(m=\frac{0.90\times145}{100}\).

First, calculate \(0.90\times145 = 130.5\). Then \(\frac{130.5}{100}=1.305\).

Step3: Round to the correct number of significant digits

The number \(0.90\) has two significant digits, and \(145\) has three significant digits. When multiplying or dividing, the result should be rounded to the least number of significant digits among the values used in the calculation. So we round \(1.305\) to two significant digits.

Answer:

\(1.3\space g\)