Question

Question:In 1987 the first substance to act as a superconductor at a temperature above that of liquidnitrogen (77 K) was discovered. The approximate formula of this substance is YBa₂Cu₃O₇. Calculate the percent composition by mass of this material.

Short answer

Answer

The percentage composition by material’s mass has been calculated.

Step-by-step solution

Calculating mass percent of the elements from the formula

The element’s mass percentage from formula can be denoted by mass comparison each element in 1 mole of compound to the total mass.

$$\begin{gathered} Mass of Y=1 mol \times 88.905 g/mol=88.905 g \\ Mass of Ba= 2 mol \times 137.32 g/mol = 274.64 g \\ Mass of Cu= 3 mol \times 63.546 g/mol = 190.638 g \\ Mass of O= 7 mol \times 15.999 g/mol=111.993 g \\ Mass of 1 mole YB{a}_{2}C{u}_3{O}_7=666.176 g \end{gathered}$$

Mass percentage of the elements

The mass percentage can be denoted as,

$$\begin{gathered} Mass \% of Y=\left[\frac{Mass of Y}{Mass of 1 mole of YB{a}_{2}C{u}_3{O}_7}\right]\times 100 \\ =\left[\frac{88.905}{666.176}\right]\times 100 \\ =13.345 \% \end{gathered}$$

Mass percentage of the elements

The mass percentage can be denoted as,

$$\begin{gathered} Mass \% Ba=\frac{274.64}{666.176}\times 100 \\ =41.22\% \\ Mass \% Cu=\frac{190.638}{666.176}\times 100 \\ =28.61\% \\ Mass \% O=\frac{111.993}{666.176}\times 100 \\ =16.81\% \end{gathered}$$