Question

A student plans to use a density versus solution concentration standard curve to identify the sodium chloride concentration in an unknown salt water solution. The unknown should have a concentration between 3.0% and 6.0% by mass of sodium chloride. If the student prepares each standard by adding some mass of sodium chloride to 30.0 grams of Dl water, which of the following mass sets of sodium chloride will result in an appropriate standard curve? Select all that apply.
a. 0.50 g, 1.0 g, 1.5 g, 2.0 g, 2.5 g
b. 2.0 g, 4.0 g, 8.0 g, 10.0 g, 12.0g
c. 0.1 g, 0.2 g, 0.3 g, 0.4 g, 1.0 g
d. 0.1 g, 0.3 g, 0.6 g, 0.9 g, 1.2 g,
e. 2.0 g, 3.0 g, 4.0 g, 5.0 g. 6,0 g
f. 0.20 g, 0.40 g, 0.80 g, 1.0 g. 1.2 g
g. 0.1g,0.5 g, 1.0 g, 1.5 g, 2.0 g

Answer 1

Answer:

a. 0.50 g, 1.0 g, 1.5 g, 2.0 g, 2.5 g;

g. 0.1 g, 0.5 g, 1.0 g, 1.5 g, 2.0 g

Explanation:

The percent mass is defined as a ratio between the mass of a solute and mass of a solution:

$\omega = \frac{m_{solute}}{m_{solution}}\cdot 100\%$

Since solution only consists of a solute and solvent, express its mass as:

$m_{solution} = m_{solute} + m_{solvent}$

Then:

$\omega = \frac{m_{solute}}{m_{solution}}\cdot 100\%=\frac{m_{solute}}{m_{solute} + m_{solvent}}$

Firstly, solve for how much mass is required to prepare 3.0 %. Let's say, we have x g of the solute:

$0.03 = \frac{x}{30.0 + x}\therefore x = 0.03(30.0 + x)$

$x = 0.90 + 0.03x$

$0.97x = 0.90\therefore x = 0.93 g$

Similarly, solve for 6.0 %, let's say, we have x g of the solute again:

$0.06 = \frac{x}{30.0 + x}\therefore x = 0.06(30.0 + x)$

$x = 1.80 + 0.06x$

$0.94x = 1.80\therefore x = 1.91 g$

Hence, masses should be in a range of 0.93 g to 1.91 g.