# What is the molarity of a #"KOH"# solution with relative density #0.0028# and #%"w/w" = 40%#? The molar mass of #"KOH"# is #"56.1056 g/mol"#.

##### 1 Answer

#c = "0.02 M"#

The *molarity* of a solution is given by

#c = "mols solute"/"L solution"# ,

so we'll need to get the solution's volume and the mols of solute.

The **relative density**, or specific gravity, is the density of the *solution* relative to that of water (it would have to be based on the solution; if it was based on the solid, it would be much higher), i.e.

#rho_"rel" = 0.0028 = rho_"soln"/rho_w#

Since the density of water is close to **percent by mass** is

#"%w/w" = "mass of solute"/"mass of solution" xx 100%# ,

we then know that for every

Using the density of the solution, its volume is:

#ul(V_"soln") = 100 cancel"g solution" xx "1 L soln"/(2.8 cancel"g soln")#

#=# #ul"35.7 L soln"#

Using the molar mass of

#ul(n_"KOH") = 40 cancel"g KOH" xx "1 mol KOH"/(56.1056 cancel"g KOH")#

#=# #ul"0.713 mols KOH"#

Therefore, the **molarity** is:

#color(blue)(c) = "0.713 mols KOH"/"35.7 L soln"#

#=# #color(blue)("0.02 M")#