Question #ccb82

1 Answer
Mar 28, 2017

Answer:

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)#