Question

Please calculate the density in g/cm3 and the molecular weight in g/mol for an XZ alloy of composition 35 wt% X and 65 wt% Z, knowing that the density of X is 6.37 g/cm3 and of Z is 8.97 g/cm3 and that molecular weights of X and Z are 53 g/mol and 87 g/mol, respectively.

Answer 1

a)
`\rho_(XZ) = 7.849\,(g)/(cm^(3))`, b)
`M_(XZ) = 75.1\,(g)/(mol)`

Step-by-step explanation:

a) Density is the ratio of the mass to the volume:

`\rho_(XZ) = (m_(X)+m_(Z))/(V_(X)+V_(Z))`

`\rho_(XZ) = (m_(X)+m_(Z))/((m_(X))/(\rho_(X))+(m_(Z))/(\rho_(Z)) )`

Let assume that material has 35 gram X and 65 gram Z. Then:

`\rho_(XZ) = (35\,g+65\,g)/((35\,g)/(6.37\,(g)/(cm^(3)) )+(65\,g)/(8.97\,(g)/(cm^(3)) ) )`

`\rho_(XZ) = 7.849\,(g)/(cm^(3))`

b) The molecular weight of the material is:

`M_(XZ) = 0.35\cdot M_(X) + 0.65\cdot M_(Z)`

`M_(XZ) = 0.35\cdot (53\,(g)/(mol) ) + 0.65\cdot (87\,(g)/(mol) )`

`M_(XZ) = 75.1\,(g)/(mol)`