What are the mass fraction and the molar concentration of glucose (#M_text(r) = 180.16#) in 320 g of a solution that contains 40 g of glucose?

#"Density of solution = 1400 kg·m"^"-3"#

1 Answer
Jul 4, 2017

Answer:

The mass fraction of glucose is 0.125. The molar concentration is #"0.97 mol/dm"^3#.

Explanation:

Mass Fraction

The mass fraction #w_i# of a component #i# in a mixture is the mass of the component #m_i# divided by the total mass #m_text(tot)#:

#color(blue)(bar(ul(|color(white)(a/a) w_i = m_i/m_text(tot)color(white)(a/a)|)))" "#

In this problem,

#m_text(glucose) = "40 g"#
#m_text(tot) = "40 g + 280 g = 320 g"#

#w_text(glucose) = (40 color(red)(cancel(color(black)("g"))))/(320 color(red)(cancel(color(black)("g")))) = 0.125#

Molar concentration

The formula for molar concentration #c# is

#color(blue)(bar(ul(|color(white)(a/a)c = "moles"/"cubic decimetres" = n/Vcolor(white)(a/a)|)))" "#

#n = 40 color(red)(cancel(color(black)("g"))) × "1 mol"/(180.16 color(red)(cancel(color(black)("g")))) = "0.222 mol"#

#V = 320 × 10^"-3" color(red)(cancel(color(black)("kg"))) × ("1 m"^3)/(1400 color(red)(cancel(color(black)("kg")))) = 2.286×10^"-4" color(white)(l)"m"^3 = "0.2286 dm"^3#

#c = "0.222 mol"/"0.2286 dm"^3 = "0.97 mol/dm"^3#