Question

\(0.24 \mathrm{~g}\) of a volatile liquid on vaporization gives \(45 \mathrm{~mL}\) of vapours at STP. What will be the vapour density of the substance? (Density of \(\mathrm{H}_{2}=0.089 \mathrm{gL}^{-1}\) ) (a) \(99.39\) (b) \(39.95\) (c) \(95.53\) (d) \(59.93\)

Short answer

The vapour density of the substance is (d) 59.93.

Step-by-step solution

Understand STP Conditions

At Standard Temperature and Pressure (STP), the volume of 1 mole of an ideal gas is 22.4 liters or 22400 milliliters.

Determine Moles of Gas at STP

We have 45 mL of gas at STP. To find the number of moles, we use the relationship: \[\text{moles} = \frac{\text{Volume at STP (mL)}}{22400} = \frac{45}{22400} = 0.00200893 \text{ moles}.\]

Calculate Molar Mass of Substance

Using the mass of the volatile liquid and the moles calculated: \[\text{Molar mass} = \frac{\text{mass (g)}}{\text{moles}} = \frac{0.24 \, \text{g}}{0.00200893 \, \text{moles}} = 119.43 \, \text{g/mol}.\]

Calculate Vapour Density

Vapour density is given by half of the molar mass of the gas, so: \[\text{Vapour density} = \frac{119.43}{2} = 59.715.\]

Match to Closest Option

Compare the calculated vapour density to the given options. Our result corresponds closest to option (d): 59.93.

Key concepts

Volatile Liquid

Volatile liquids are substances that can easily evaporate at room temperature, turning from a liquid to a gas. This property is crucial in understanding the behavior of gases in chemical reactions.
Volatility is determined by how much vapor a liquid produces in the air, and it depends largely on the intermolecular forces of the liquid. Weaker forces mean higher volatility.

• Volatility impacts vapor pressure: higher volatility results in higher vapor pressure.
• The process of a volatile liquid becoming a vapor is essential in calculations involving gas phase reactions.

Understanding how a volatile liquid behaves helps predict how it will interact with other chemicals, particularly in reactions involving gases at various conditions.

STP Conditions

STP stands for Standard Temperature and Pressure, a set of conditions often used in chemistry to allow for easy comparison between gas behaviors. At STP:

• Temperature is 0°C (273.15 K).
• Pressure is 1 atmosphere (101.3 kPa).
• One mole of an ideal gas occupies 22.4 liters or 22400 milliliters.

These consistent conditions simplify calculations involving gases. By knowing the volume of a gas at STP, you can directly calculate the moles using the conversion:\[ \text{moles} = \frac{\text{Volume at STP (mL)}}{22400} \]
This is crucial in determining characteristics like molar mass or gas density.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, a fundamental concept when working with chemical reactions. It is typically expressed in grams per mole (g/mol).
To calculate molar mass, you need the mass of the substance and the number of moles present:\[ \text{Molar mass} = \frac{\text{mass (g)}}{\text{moles}} \]
In our example, the mass of the volatile liquid is 0.24 g and the calculated moles at STP were 0.00200893, leading to a molar mass of 119.43 g/mol.

• A correct calculation of molar mass helps to identify substances by comparing with known values.
• It is also used in computing other properties, such as vapor density, which is half of the molar mass for gases.

Understanding how to accurately calculate molar mass is critical in studying stoichiometry and chemical compound formulation.