Question

Wood’s metal contains $50\%$ bismuth, $25\%$ lead, $12.5\%$ tin and $12.5\%$ cadmium by weight. What is the mole fraction of tin?
Atomic weights: $\left( {Bi = 209;Pb = 207;Sn = 119;Cd = 112} \right)$
A.$0.202$
B.$0.158$
C.$0.176$
D.$0.221$

Answer 1

An alloy is a mixture of two or more chemical elements. The mole fraction of a compound can be calculated from the moles of the compound to the total number of moles of the mixture. Moles are calculated from the weight and molar mass of the compound.Now in order to find the mole fraction we'll first find the number of moles of tin and then total moles of the mixture and with the help of that we can have our solution.

Complete answer:
Given that wood consists of bismuth, lead, tin and cadmium. The weight given in percentages.
Bismuth has the weight of $50\%$ , lead has the weight of $25\%$, tin has the weight of $12.5\%$ and cadmium has the weight of $12.5\%$.
The atomic weights is known as molar mass bismuth has the molar mass of $209$ , lead has the molar mass of $207$ , tin has the molar mass of $119$ , and cadmium has the molar mass of $112$ .
The number of moles of tin is $\dfrac{{12.5}}{{119}}$ moles.
The mole fraction can be calculated from the moles of tin divided by the total moles of the mixture.
The total moles of the mixture is $\dfrac{{50}}{{209}} + \dfrac{{25}}{{207}} + \dfrac{{12.5}}{{119}} + \dfrac{{12.5}}{{112}}$
The mole fraction of tin is $\dfrac{{\dfrac{{12.5}}{{119}}}}{{\dfrac{{50}}{{209}} + \dfrac{{25}}{{207}} + \dfrac{{12.5}}{{119}} + \dfrac{{12.5}}{{112}}}} = 0.176$
Thus, the mole fraction of tin is $0.176$.
Option C is the correct one.

Note:
Mole fraction is the ratio of the moles of solute and total mixture. As it is a ratio, the mole fraction has no units. Moles can be obtained from the weight and molar mass. So, the molar mass should be taken clearly as all the elements do not have molar mass which is double to atomic number.