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}."
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