Answer
$7.16\;m\;CH_3OH$
Work Step by Step
molality = mol solute / kg solvent
Since methanol is dissolved in acetonitrile, methanol is the solute and acetonitrile is the solvent.
First, calculate moles of methanol (molar mass = 32.04 g/mol).
$\frac{22.5\;mL\;CH_3OH}{}(\frac{0.791\;g}{1\;mL})(\frac{1\;mol}{32.04\;g})=0.5555\;mol\;CH_3OH$
Next, calculate kg acetonitrile.
$\frac{98.7\;mL\;CH_3CN}{}(\frac{0.786\;g}{1\;mL})(\frac{1\;kg}{1000\;g})=0.7758\;kg\;CH_3CN$
Next, calculate molality.
$\frac{0.5555\;mol\;CH_3OH}{0.7758\;kg\;CH_3CN}=7.16\;m\;CH_3OH$
