Question

\(10 \mathrm{~g}\) of hydrogen fluoride gas occupy \(5.6\) litres of volume at NTP. The empirical formula of the gas is HF. The molecular formula of the gas will be (at. wt. of fluorine \(=19)\) (1) \(\mathrm{H}_{4} \mathrm{~F}_{4}\) (2) \(\mathrm{HF}\) (3) \(\mathrm{H}_{2} \mathrm{~F}_{2}\) (4) \(\mathrm{H}_{3} \mathrm{~F}_{3}\)

Short answer

The molecular formula of the gas is HF.

Step-by-step solution

Determine the molar mass of the empirical formula (HF)

The empirical formula of the gas is HF. The atomic mass of hydrogen (H) is 1 g/mol, and the atomic mass of fluorine (F) is 19 g/mol. Therefore, the molar mass of HF is: \[M_{HF} = 1 + 19 = 20 \text{ g/mol}\]

Calculate the number of moles of HF

Given the mass of the hydrogen fluoride gas is 10 g. Using the molar mass of HF calculated in Step 1, the number of moles (n) of HF can be determined using the formula: \[n = \frac{\text{mass}}{\text{molar mass}} = \frac{10}{20} = 0.5 \text{ mol} \]

Use the ideal gas law to verify molecular formula

At NTP (Normal Temperature and Pressure), which is 1 atm pressure and 0°C (273.15 K), 1 mole of any ideal gas occupies 22.4 litres. Given that 0.5 moles of HF occupy 5.6 litres, we can see if this is consistent with the molar volume.Since: \[0.5 \text{ mol} \times 22.4 \text{ L/mol} = 11.2 \text{ L}\]Given that our volume is 5.6 litres and we calculated for 11.2 litres, we confirm that 5.6 litres is half the volume of what one mole would occupy if it's ideal.This confirms that the molecular formula remains the same - HF.

Key concepts

Empirical Formula

The empirical formula is a simplified representation of the proportions of elements in a compound. It gives the simplest whole-number ratio of atoms in the molecule. For example, in the given exercise, the empirical formula of hydrogen fluoride gas is HF. This means that, in its simplest form, each molecule of the gas contains one atom of hydrogen and one atom of fluorine.

The empirical formula does not provide information about the actual number of atoms in a molecule (which is given by the molecular formula). Instead, it provides a foundational understanding of the relative quantities of the constituent elements. To determine the empirical formula of a compound, one usually needs to know the percentage composition or the masses of the elements in a sample. The steps to determine the empirical formula are:

• Convert the mass of each element to moles using their respective atomic masses.
• Determine the simplest whole-number ratio of the moles of each element.
• Write the empirical formula using these ratios.

In this specific exercise, it's already provided that the empirical formula of the gas is HF.

Molar Mass Calculation

Molar mass is a critical concept in chemistry. It represents the mass of one mole of a substance, be it an element or a compound. The molar mass of a molecule is obtained by summing the atomic masses of all the atoms in its empirical or molecular formula. For this problem, we focus on hydrogen fluoride (HF). The atomic masses are 1 g/mol for hydrogen and 19 g/mol for fluorine. Thus, the molar mass of HF can be calculated as follows:

\(M_{HF} = 1 \text{ g/mol} + 19 \text{ g/mol} = 20 \text{ g/mol}\).
Once we have the molar mass, we can use it to find the number of moles of the compound present in a given mass. For instance, given 10 grams of HF, the number of moles, denoted as \(n\), is calculated using the formula: \(n = \frac{ \text{mass}}{\text{molar mass}} = \frac{10}{20} = 0.5 \text{ mol}\).

The molar mass is essential for connecting the macroscopic measurements we can take in the lab (like mass) to the microscopic world of molecules and atoms.

Ideal Gas Law

The Ideal Gas Law is a key equation in chemistry that relates the pressure, volume, temperature, and number of moles of an ideal gas. The law can be written as:

equation: \(PV = nRT\)

where:

• \(P\) is the pressure of the gas
• \(V\) is the volume of the gas
• \(n\) is the number of moles of the gas
• \(R\) is the universal gas constant (0.0821 L·atm/(K·mol))
• \(T\) is the temperature in Kelvin

In this exercise, we use the fact that at Normal Temperature and Pressure (NTP), which is 1 atmosphere (atm) pressure and 0°C (273.15K), one mole of any ideal gas occupies 22.4 liters (L). Given 0.5 moles of HF, we can determine its volume at NTP by multiplying the number of moles by the molar volume: \(0.5 \text{ mol} \times 22.4 \text{ L/mol} = 11.2 \text{ L}\).
In the problem, 0.5 moles of HF actually occupy 5.6 liters, which aligns perfectly since 5.6 liters is half of 11.2 liters. This verifies the volume is consistent with the ideal gas behavior and confirms that our molecular formula remains HF.