Question

a. 50 g of gasoline are mixed with 50 g of water. What is the average density of the mixture?
b. 50 cm³ of gasoline are mixed with 50 cm³ of water. What is the average density of the mixture?

Short answer

a) 837 kg/m³

b) 860 kg/m³

Step-by-step solution

Part(a) Step1 : Given information

50 g of gasoline are mixed with 50 g of water.

Part(a) Step 2 : Explanation

Average density can be calculated by

avg density = Total mass / Total volume

Total mass = 50 + 50 = 100 gm = 0.1 kg

Find total volume

Density of water = 1000 kg/ m³

Density of gasoline = 719.7 kg/ m3
Volume of gasoline $=\frac{0.05}{719.7}=6.95\times {10}^{-5}{\mathrm{m}}^3$
Volume of water $=\frac{0.05}{1000}=5\times {10}^{-5}{\mathrm{m}}^3$

Total volume = 11.95 x 10^-5 m³

$Avg.Density=\frac{0.100}{11.95x{10}^{-5}}=836.8kg/m^3$

Part(b) Step 1: Given information

50 cm³ of gasoline are mixed with 50 cm³ of water is mixed

Part(b) Step2: Explanation

Average density can be calculated by

avg density = Total mass / Total volume

Total volume = 50 cm³+ 50 cm³= 100 cm³= 10^-4m³

Now find mass

Mass of gasoline $=50\times {10}^{-6}\times 719.7=3.6\times {10}^{-2}\mathrm{kg}$
Mass of water $=50\times {10}^{-6}\times 1000=5\times {10}^{-2}\mathrm{kg}$

Total mass = 8.6 x 10^-2 kg

$AvgDensity=\frac{8.6x{10}^{-2}}{{10}^{-4}}=860kg/m^3$

So density is 860 kg/m³