Question

Question #ccb82

Answer 1

Here's what I got.

Explanation:

The density of the solution can be found by dividing its total mass by its total volume.

You can safely assume that dissolving `"2 g"` of sodium chloride in `"500 mL"` of water will not change the volume of the solution, so right from the start, you know that

`V_"solution" = V_"water" = "500 mL"`

Now, you know the mass of sodium chloride, which is the solute, so you must figure out the mass of the water, which is the solvent.

Using the fact that

`color(blue)(ul(color(black)("1 mL" = "1 cm"^3)))`

and that water has a density of `"1 g cm"^(-3)`, you can say that `"500 mL"` of water have a mass of

`500 color(red)(cancel(color(black)("mL"))) * (1color(red)(cancel(color(black)("cm"^3))))/(1color(red)(cancel(color(black)("mL")))) * "1 g"/(1color(red)(cancel(color(black)("cm"^3)))) = "500 g"`

Therefore, the total mass of the solution will be

`m_"total" = m_"NaCl" + m_"water"`

which in your case is

`m_"total" = "2 g + 500 g"`

`m_"total" = "502 g"`

The density of the solution, `rho_"sol"`, will be equal to

`rho_"sol" = m_"total"/V_"solution"`

Plug in your values to find

`rho_ "sol" = "502 g"/"500 mL" = "1.004 g mL"^(-1)`

Now, I'll leave the answer rounded to four sig figs, but keep in mind that it should be rounded to one significant figure.

So the correct answer here would be

`rho_"sol" = "1 g mL"^(-1)`