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2 years ago

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A gaseous compound is 78.14 percent boron and 21.86 percent hydrogen. At 27°C, 74.3 mL of the gas exerted a pressure of 1.12 atm

. If the mass of the gas was 0.0934 g, what is its molecular formula?

1 answer:

KonstantinChe [14]2 years ago

3 0

Answer:

B₂H₆

Explanation:

Given parameters:

Mass percentage of hydrogen = 21.86%

Mass percentage of boron = 78.14%

Temperature of the compound = 27°C

Pressure exerted by the gas = 1.12atm

Volume of the gas = 74.3mL = 0.0743L or 0.0743dm³

Mass of the gas = 0.0934g

Unknown:

Molecular formula of the gas = ?

We have to convert the temperature to a unit we can work with which is Kelvin:

27°C to K gives 273 + 27, which is 300K

Solution

From the mass percentages, we can derive the empirical formula of the compound.

The empirical formula is the simplest formula of a compound.

The procedure is shown below:

B H

Mass precentage 78.14 21.86

Number of moles 78.14/10.8 21.86/1

7.24 21.86

Dividing by the

smallest 7.24/7.24 21.86/7.24

1 3

The empirical formula of the compound is BH₃

To derive the molecular formula:

M.F = (E.F) x n

n is the number of repeating units of the empirical formula present in one mole.

To find the molecular formula of the gas, we use the ideal gas law to obtain the number of moles of the gas. We then proceed to find the molar mass.

ideal gas law: PV = nRT

The unknown is n, and we make it the subject of the expression:

n = $\frac{PV}{RT}$

Where P is pressure of the gas

V is the volume of the gas

R is the gas constant which is given as 0.082atmdm³mol⁻¹K⁻¹

T is the temperature

n = $\frac{1.12 x 0.0743}{0.082 x 300}$

n = 0.0034mole

From the expression:

number of moles = $\frac{mass}{molar mass}$

molar mass = $\frac{mass}{number of moles}$

molar mass = $\frac{0.0934}{0.0034}$

molar mass = 27.5g/mol of the molecular formula

From M.F = (E.F) x n we need to solve for n:

E.F is BH₃ this gives a mass of [10.8 + 3(1)] = 13.8g/mol

n = $\frac{molecular mass of the molecular formula}{molecular mass of the empirical formula}$

n = $\frac{27.5}{13.8}$ = 2

Molecular formula of the compound is then (BH₃)₂ which gives B₂H₆

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