Question

Patients undergoing an upper gastrointestinal tract laboratory test are typically given an X-ray contrast agent that aids with the radiologic imaging of the anatomy. One such contrast agent is sodium diatrizoate, a nonvolatile water-soluble compound. A 0.378-m solution is prepared by dissolving 38.4 g of sodium diatrizoate (NaDTZ) in $\mathbf{1}\mathbf{.}\mathbf{60}\mathbf{\times }{\mathbf{10}}^2\mathbf{ml}$ of water at 31.28C (the density of water at $\mathbf{31}\mathbf{.}{\mathbf{28}}^o\mathbf{C}$ is 0.995 g/mL). What is the molar mass of sodium diatrizoate? What is the vapor pressure of this solution if the vapor pressure of pure water at $\mathbf{31}\mathbf{.}{\mathbf{28}}^o\mathbf{C}$ is 34.1 torr?

Short answer

The molar mass ofsodium diatrizoate is 640g/mol.

The vapor pressure is 33.9torr.

Step-by-step solution

Step 1:

First, calculate the mass and moles of water.

$mass=d\times V=0.995g/mL\times 160mL=0.159kg$

$n=\frac{\text{mass}}{molarmass}=\frac{159g}{18.016}=8.83mol$

Step 2:

Calculate the number of moles from molarity.

$\begin{array}{c}m=\frac{n\left(NaDTZ\right)}{mass\left(H_{2}O\right)}\\ n\left(NaDTZ\right)=m\times mass\left(H_{2}O\right)\\ =0.378mol/kg\times 0.159kg=0.060mol.\end{array}$

Step 3:

Use Raoult’s lawto calculate the vapor pressure of the solution.

$P_{so\ln }=0.993\times 34.1tprr=33.9torr$