Question

Calculate the percentage composition of chromium in potassium dichromate, ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$.

$\left[\mathrm{K}=39,\mathrm{Cr}=52,\mathrm{O}=16\right]$

Answer 1

Step 1: Given information:

• The given compound is Potassium dichromate, ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$.
• The mass of the Potassium $\left(\mathrm{K}\right)$ element$=39\mathrm{g}$
• The mass of the Chromium $\left(\mathrm{Cr}\right)$ element$=52\mathrm{g}$
• The mass of the Oxygen $\left(\mathrm{O}\right)$ element$=16\mathrm{g}$

Step 2: Calculate the molecular mass of ${\mathbf{K}}_{\mathbf{2}}{\mathbf{Cr}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{7}}$

• To determine the molecular mass, multiply the number of atoms by the mass of that element and sum the masses of all the elements of the compound.
• The molecular mass of ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$ is manipulated as follows:

$$\begin{gathered} \mathrm{Molecular}\mathrm{mass}\mathrm{of}{\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7=39\mathrm{g}\times 2+52\mathrm{g}\times 2+16\mathrm{g}\times 7 \\ =294\mathrm{g} \end{gathered}$$

Step 3: Calculation of percentage composition

• Use the following formula to calculate the percentage composition of hydrogen.

$\mathrm{Percentage}\mathrm{composition}\mathrm{by}\mathrm{mass}=\frac{\mathrm{Mass}\mathrm{of}\mathrm{the}\mathrm{element}\mathrm{in}\mathrm{one}\mathrm{molecule}\mathrm{of}\mathrm{a}\mathrm{compound}}{\mathrm{Gram}\mathrm{molecular}\mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{compound}}\times 100\mathrm{g}$

Step 4: Calculate the percentage composition of Chromium

• $294\mathrm{g}$ of ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$ contains $52\mathrm{g}\times 2=104\mathrm{g}$ Chromium.
• Therefore, $100\mathrm{g}$ ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$ will contain $\frac{104\mathrm{g}}{294\mathrm{g}}\times 100\mathrm{g}=35.37\mathrm{g}$ Chromium.

Thus, the required percentage composition of chromium is $35.37\%$.