Chapter 10, Problem 200A

Interpretation Introduction

Interpretation:

A bar graph must be designed to indicate the mole of each element in 5.67 carat YAG where 1 carat is 0.2 g.

Concept introduction:

The number of moles can be calculated from mass and molar mass as follows:

Mole of any substance $\text{=}\frac{\text{mass}}{\text{molar mass}}\text{.}$

Answer to Problem 200A

Bar graph is shown below to indicate the mole of each element as present in 5.67 carat YAG.

Explanation of Solution

Molar mass of YAG (Y₃Al₅O₁₂) is 594 g/mol

Thus it can be said that one mole of YAG contains 3 moles of Y, 5 moles of Al and 12 moles of O respectively.

5.67 carat YAG $\text{=5}\text{.67×0}\text{.2 g=1}\text{.134 g}\text{.}$

594 g YAG contains 3 moles Y.

Thus,

1 g YAG contains $\frac{3}{594}$ mole Y.

Or,

1.134 g YAG contains $\frac{\text{3×1}\text{.134}}{\text{594}}\text{ mole = 0}\text{.006 mole}\text{.}$ Y.

Similarly,

594 g YAG contains 5 moles Al.

Thus,

1 g YAG contains $\frac{5}{594}$ mole Al.

And,

1.134 g YAG contains $\frac{\text{5×1}\text{.134}}{\text{594}}\text{ mole = 0}\text{.010 mole}$ Al.

Now,

594 g YAG contains 12 moles O.

Thus,

1 g YAG contains $\frac{12}{594}$ mole O.

And,

1.134 g YAG contains $\frac{\text{12×1}\text{.134}}{\text{594}}\text{ mole = 0}\text{.023 mole}$ O.

These moles are used to make the bar graph as follows:

Conclusion

Thus, 5.67 cart YAG contains 0.006 mole Y, 0.010 mole Al and 0.023 mole O which are depicted in the bar graph.