A laboratory technician is preparing a calibration standard by mixing two liquids. A volume V1 V_1\,V1 of Liquid 1 (density ρ1\rho_1ρ1) is mixed thoroughly with a mass m2 m_2\,m2 of Liquid 2 (density ρ2\rho_2ρ2) to form a single, uniform solution.
Assuming the total volume of the mixture is exactly equal to the sum of the individual volumes of the two liquids, which of the following is the correct expression for the density of the mixture, ρmix\rho_{\text{mix}}ρmix?
ρmix=ρ1V1+m2V1+ρ2m2
\rho_{\text{mix}} = \frac{\rho_1 V_1 + m_2}{V_1 + \rho_2 m_2}
ρmix=V1+ρ2m2ρ1V1+m2
ρmix=ρ2(ρ1V1+m2)ρ2V1+m2
\rho_{\text{mix}} = \frac{\rho_2 (\rho_1 V_1 + m_2)}{\rho_2 V_1 + m_2}
ρmix=ρ2V1+m2ρ2(ρ1V1+m2)
ρmix=ρ1V1+m2V1+m2
\rho_{\text{mix}} = \frac{\rho_1 V_1 + m_2}{V_1 + m_2}
ρmix=V1+m2ρ1V1+m2
ρmix=ρ2(ρ1V1+m2)ρ1V1+m2
\rho_{\text{mix}} = \frac{\rho_2 (\rho_1 V_1 + m_2)}{\rho_1 V_1 + m_2}
ρmix=ρ1V1+m2ρ2(ρ1V1+m2)