Question

If 21g alcohol of density 0.7g/cm³ is mixed with 10g of water, what would be the density of the resulting mixture

Answer 1

Let's first find the volumes of alcohol and water, respectively:

$$V_{alcohol} = \dfrac{m_{alcohol}}{\rho_{alcohol}} = \dfrac{21g}{0.7 \dfrac{g}{cm^3}} = 30 cm^{3},$$ $$V_{water} = \dfrac{m_{water}}{\rho_{water}} = \dfrac{10g}{1.0 \dfrac{g}{cm^3}} = 10 cm^{3}.$$

Then, we can calculate the volume of the mixture and its mass:

$$V_{mixture} = V_{alcohol} + V_{water} = 30cm^3 + 10cm^3 = 40cm^3,$$ $$m_{mixture} = m_{alcohol} + m_{water} = 21g + 10g = 31g.$$

Finally, we can calculate the density of the resulting mixture:

$$\rho_{mixture} = \dfrac{m_{mixture}}{V_{mixture}} = \dfrac{31g}{40cm^3} = 0.775 \dfrac{g}{cm^3}.$$

Answer:

$\rho_{mixture} = 0.775 \dfrac{g}{cm^3}.$