Find the Mass Percentages Ca_5(PO_4)_3(OH)

$C a_{5} {(P O_{4})}_{3} (O H)$

Step 1

To find the mass of $1$ mole of $C a_{5} {(P O_{4})}_{3} (O H)$ look up the atomic mass of each element and multiply it by the number of atoms contained in each element in the molecule.

mass of $1$ mole of $C a_{5} {(P O_{4})}_{3} (O H)$ $=$ $5 (mass of Ca)$ + $3 (mass of P)$ + $12 (mass of O)$ + $(mass of O)$ + $(mass of H)$

Step 2

Fill in the atomic masses from the periodic table.

mass of $1$ mole of $C a_{5} {(P O_{4})}_{3} (O H)$ $=$ $5 (40.08000183)$ + $3 (30.96999931)$ + $12 (16)$ + $(16)$ + $(1.00999999)$

Step 3

Simplify the result.

Remove parentheses.

mass of $1$ mole of $C a_{5} {(P O_{4})}_{3} (O H) = 5 (40.08000183) + 3 (30.96999931) + 12 (16) + 16 + 1.00999999 g$

Simplify each term.

Multiply $5$ by $40.08000183$ .

mass of $1$ mole of $C a_{5} {(P O_{4})}_{3} (O H) = 200.40000915 + 3 (30.96999931) + 12 (16) + 16 + 1.00999999 g$

Multiply $3$ by $30.96999931$ .

mass of $1$ mole of $C a_{5} {(P O_{4})}_{3} (O H) = 200.40000915 + 92.90999794 + 12 (16) + 16 + 1.00999999 g$

Multiply $12$ by $16$ .

mass of $1$ mole of $C a_{5} {(P O_{4})}_{3} (O H) = 200.40000915 + 92.90999794 + 192 + 16 + 1.00999999 g$

Simplify by adding numbers.

Add $200.40000915$ and $92.90999794$ .

mass of $1$ mole of $C a_{5} {(P O_{4})}_{3} (O H) = 293.31000709 + 192 + 16 + 1.00999999 g$

Add $293.31000709$ and $192$ .

mass of $1$ mole of $C a_{5} {(P O_{4})}_{3} (O H) = 485.31000709 + 16 + 1.00999999 g$

Add $485.31000709$ and $16$ .

mass of $1$ mole of $C a_{5} {(P O_{4})}_{3} (O H) = 501.31000709 + 1.00999999 g$

Add $501.31000709$ and $1.00999999$ .

mass of $1$ mole of $C a_{5} {(P O_{4})}_{3} (O H) = 502.32000708 g$

Step 4

Find the mass percentage of $C a$ .

The mass composition percentage is the mass of $C a$ divided by the mass of the entire molecule converted to a percentage.

Mass percentage of $C a = \frac{200.4}{502.32000708} \cdot 100$

Divide $200.4$ by $502.32000708$ .

$0.39894887 \cdot 100$

Multiply $0.39894887$ by $100$ .

$39.89488715$

Set the number as a percent.

Mass percentage of $C a = 39.89488715 %$

Step 5

Find the mass percentage of $P$ .

The mass composition percentage is the mass of $P$ divided by the mass of the entire molecule converted to a percentage.

Mass percentage of $P = \frac{92.91}{502.32000708} \cdot 100$

Divide $92.91$ by $502.32000708$ .

$0.18496177 \cdot 100$

Multiply $0.18496177$ by $100$ .

$18.49617747$

Set the number as a percent.

Mass percentage of $P = 18.49617747 %$

Step 6

Find the mass percentage of $O$ .

The mass composition percentage is the mass of $O$ divided by the mass of the entire molecule converted to a percentage.

Mass percentage of $O = \frac{208}{502.32000708} \cdot 100$

Divide $208$ by $502.32000708$ .

$0.41407866 \cdot 100$

Multiply $0.41407866$ by $100$ .

$41.40786691$

Set the number as a percent.

Mass percentage of $O = 41.40786691 %$

Step 7

Find the mass percentage of $H$ .

The mass composition percentage is the mass of $H$ divided by the mass of the entire molecule converted to a percentage.

Mass percentage of $H = \frac{1.01}{502.32000708} \cdot 100$

Divide $1.01$ by $502.32000708$ .

$0.00201067 \cdot 100$

Multiply $0.00201067$ by $100$ .

$0.20106704$

Set the number as a percent.

Mass percentage of $H = 0.20106704 %$

Step 8

Find the mass percentage of each element in the molecule.

Mass percentage of $C a = 39.89488715 %$

Mass percentage of $P = 18.49617747 %$

Mass percentage of $O = 41.40786691 %$

Mass percentage of $H = 0.20106704 %$

Find the Mass Percentages Ca_5(PO_4)_3(OH)

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