Question

Potassium hydrogen phthalate is a primary standard used to measure the concentration ofsolutions. Find the true mass of potassium hydrogen phthalate (density $\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{636}\mathbf{g}\mathbf{/}\mathbf{mL}$) if the mass weighed in air is. If you did not correct the mass$\mathbf{4}\mathbf{.}\mathbf{2366}\mathbf{g}$ ass for buoyancy, would the calculated morality ofbe too high or too low? By what percentage?

Short answer

The required mass is 4.2391g , which is lowered by 0.06%.

Step-by-step solution

Defining density

The mass of a material substance per unit volume is called density. Density is calculated using the formula d = M/V, where d represents density, M is mass, and V is volume.

Applying the formula for buoyancy

Buoyancy corrections are weight measurements that are adjusted by estimating the difference in densities between the standard and unknown weights.

We will apply the formula for buoyancy adjustment given below. Here, $d_a$ stands for the density of air, whereas $d_o$stands for the density of the weighed product in the air.

$m=\frac{m\left(1{\displaystyle \frac{d_a}{d_w}}\right)}{\left(1\frac{d_a}{d_o}\right)}$

Finding the true mass of potassium hydrogen phthalate

In order to find the true mass of potassium hydrogen phthalate (density = 1.636g/mL), we will use the mass weighed in air, which is 4.2366g.

$$\begin{gathered} m=4.2366g\times \frac{(1-\left(0.0012g/mL/8g/mL\right)}{1-(0.0012g/mL/1.636g/mL} \\ =4.2391g \end{gathered}$$.

The mass of potassium hydrogen phthalate weighed in the air should then be subtracted from the mass corrected:

$$\begin{gathered} 4.2366g-4.2391g \\ =2.5\times {10}^{-3}g\left(2.5\times {10}^{-3}g\right)/4.2366g \\ =\left(5.9\times {10}^{-4}\right)\times 100 \\ =0.06\% \end{gathered}$$

Thus, the required mass is 4.2391g , which is lower by 0.06%