Question

a chemist prepares a solution of calcium sulfate (caso₄) by weighing out 0.647 mg of calcium sulfate into a 350 ml volumetric flask and filling the flask to the mark with water.
calculate the concentration in g/dl of the chemists calcium sulfate solution. be sure your answer has the correct number of significant digits.

Explanation:

Step1: Convert mass from mg to g

We know that \(1\space g = 1000\space mg\). So, for \(m = 0.647\space mg\), the mass in grams is \(m=\frac{0.647}{1000}\space g=6.47\times 10^{-4}\space g\)

Step2: Convert volume from mL to dL

We know that \(1\space dL=100\space mL\). So, for \(V = 350\space mL\), the volume in deciliters is \(V=\frac{350}{100}\space dL = 3.5\space dL\)

Step3: Calculate the concentration

The concentration \(C\) (in \(g/dL\)) is given by the formula \(C=\frac{m}{V}\). Substituting \(m = 6.47\times 10^{-4}\space g\) and \(V = 3.5\space dL\), we get \(C=\frac{6.47\times 10^{-4}}{3.5}\space g/dL\approx1.85\times 10^{-4}\space g/dL\)

Answer:

\(1.9\times 10^{-4}\space g/dL\) (rounded to two significant digits as \(0.647\) has three significant digits and \(350\) has two significant digits, and we follow the rule of significant - digit for division)