Question

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"`

Answer 1

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`