Question

calculate the molarity of a solution of ethanol in water in which mole fraction of with ethanol is 0.040

Answer 1

Moles of ethanol = 0.04 mol
Moles of water = 1 - 0.04 = 0.96 mol

Mass of water = 0.96 * 18 = 17.3g
Mass of ethanol = 0.04 * 46 = 1.84g

Mass of solution = 17.3 + 1.84 = 19.1g
Let density of solution be 1g/ml

Volume of solution = mass/density = 19.1/1 = 19.1ml = 0.0191L

Molarity = 0.04/0.0191 = 2.1M

Answer 2

Answer:The molarity of a solution of ethanol in water is 2.0429mol/L

Explanation;

Mole fraction of ethanol $\chi_e=0.040$

Mole fraction of water = $\chi_w=1-\chi_e=1-0.040=0.960$

Moles of ethanol = 0.040 moles

Mass of 0.040 moles of ethanol=$0.040 mole\times 46 g/mol=1.86 g$

Density of ethanol =0.789 g/mL

Volume of ethane =$\frac{1.86 g}{0.789 g/mL}=2.357 mL=0.0023 L$

Moles of water = 0.960 moles

Mass of 0.960 moles of water =$0.960 mol\times 18 g/mol=17.28 g$

Density of water = 1g/mL

Volume of water =$\frac{17.28 g}{1 g /mL}=17.28 ml=0.01728 L$

$\frac{\text{moles of ethanol}}{\text{total volume of Solution}}</p><p>[tex]Molarity=\frac{0.040 mol}{0.01728 L+0.0023L}=2.0429 mol/L$

The molarity of a solution of ethanol in water is 2.0429 mol/L.