Answer:
a) [tex]\rho_{XZ} = 7.849\,\frac{g}{cm^{3}}[/tex], b) [tex]M_{XZ} = 75.1\,\frac{g}{mol}[/tex]
Explanation:
a) Density is the ratio of the mass to the volume:
[tex]\rho_{XZ} = \frac{m_{X}+m_{Z}}{V_{X}+V_{Z}}[/tex]
[tex]\rho_{XZ} = \frac{m_{X}+m_{Z}}{\frac{m_{X}}{\rho_{X}}+\frac{m_{Z}}{\rho_{Z}} }[/tex]
Let assume that material has 35 gram X and 65 gram Z. Then:
[tex]\rho_{XZ} = \frac{35\,g+65\,g}{\frac{35\,g}{6.37\,\frac{g}{cm^{3}} }+\frac{65\,g}{8.97\,\frac{g}{cm^{3}} } }[/tex]
[tex]\rho_{XZ} = 7.849\,\frac{g}{cm^{3}}[/tex]
b) The molecular weight of the material is:
[tex]M_{XZ} = 0.35\cdot M_{X} + 0.65\cdot M_{Z}[/tex]
[tex]M_{XZ} = 0.35\cdot (53\,\frac{g}{mol} ) + 0.65\cdot (87\,\frac{g}{mol} )[/tex]
[tex]M_{XZ} = 75.1\,\frac{g}{mol}[/tex]
