Question 25
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
Reference: Past Exam Paper – June 2018 Paper 13 Q13
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
Thanks for this! :)
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