Question

compound x has a molar mass of 283.89 g·mol⁻¹ and the following composition:
element mass %
phosphorus 43.64%
oxygen 56.36%
write the molecular formula of x.

Explanation:

Step1: Calculate moles of each element

Assume 100 g of the compound.

• Moles of phosphorus ($P$): $n_{P}=\frac{43.64\ g}{30.97\ g/mol}\approx1.41\ mol$
• Moles of oxygen ($O$): $n_{O}=\frac{56.36\ g}{16.00\ g/mol}\approx3.52\ mol$

Step2: Find the ratio of moles

Divide each mole value by the smaller mole value (1.41).

• Ratio for $P$: $\frac{1.41}{1.41} = 1$
• Ratio for $O$: $\frac{3.52}{1.41}\approx2.5$

Multiply by 2 to get whole - number ratio. So, $P:O = 2:5$. The empirical formula is $P_{2}O_{5}$.

Step3: Calculate the empirical formula mass

Empirical formula mass of $P_{2}O_{5}$: $(2\times30.97)+(5\times16.00)=61.94 + 80=141.94\ g/mol$

Step4: Find the multiple ($n$)

$n=\frac{\text{Molar mass of compound}}{\text{Empirical formula mass}}=\frac{283.89\ g/mol}{141.94\ g/mol}\approx2$

Step5: Determine the molecular formula

Multiply the empirical formula by $n$. Molecular formula: $(P_{2}O_{5})\times2 = P_{4}O_{10}$

Answer:

$P_{4}O_{10}$