Q#25 (Past Exam Paper – June 2018 Paper 13 Q13)
Full-fat milk is made up of fat-free milk mixed with fat.
A volume of 1.000 × 10-3 m3 of full-fat milk has a mass of 1.035 kg. It contains 4.00% fat by volume.
The density of fat-free milk is 1.040 × 103 kg m-3.
What is the density of fat?
A 1.25 × 102 kg m-3
B 9.15 × 102 kg m-3
C 9.28 × 102 kg m-3
D 1.16 × 103 kg m-3
Solution:
Answer: B.
Density of full-fat milk = total mass / total volume
Total mass = mass of fat + mass of fat-free milk
Total volume = volume of fat + volume of fat-free milk
Density of full-fat milk = mass / volume = 1.035 / (1.000×10-3) = 1035 kg m-3
The full fat milk contains 4.00% fat by volume.
Volume of fat = 0.04 × 1.000×10-3 = 4.0×10-5 m3
Volume of fat-free milk = (96% =) 0.96 × 1.000×10-3 = 9.6×10-4 m3
Given that density of fat-free milk = 1.040×103 kg m-3,
Mass of fat-free milk = ρV = 1.040×103 × 9.6×10-4 = 0.9984 kg
{Note that we need to consider all the significant figures available as data given in the question indicate this (1.000×10-3 is given instead of 1.0×10-3).}
Total mass = mass of fat + mass of fat-free milk
Mass of fat = 1.035 – 0.9984 = 0.0366 kg
Density of fat = mass / volume
Density of fat = 0.0366 / 4.0×10-5 = 915 = 9.15×102 kg m-3
Post a Comment for "Full-fat milk is made up of fat-free milk mixed with fat. A volume of 1.000"