Finding Molecular Weight from Gas Volume at NTP

The question asks us to determine the molecular weight of a gas X given its mass and volume at Normal Temperature and Pressure (NTP).

Understanding NTP Conditions

NTP stands for Normal Temperature and Pressure. Under NTP conditions:

• Temperature = 0°C or 273.15 K
• Pressure = 1 atmosphere (atm)

A key concept for gases at NTP is the molar volume. One mole of any ideal gas occupies a volume of 22.4 litres at NTP.

Given Information

• Mass of gas X = 10 g
• Volume of gas X at NTP = 5.6 litres

Step-by-Step Calculation of Molecular Weight

Step 1: Calculate the number of moles of gas X.

We know the volume of the gas at NTP and the molar volume at NTP (22.4 L/mol). We can use the formula:

$$ \text{Number of moles} = \frac{\text{Volume at NTP}}{\text{Molar Volume at NTP}} $$

Substituting the given values:

$$ \text{Number of moles} = \frac{5.6 \text{ L}}{22.4 \text{ L/mol}} $$

Let's perform the division:

$$ \text{Number of moles} = \frac{5.6}{22.4} = \frac{56}{224} = \frac{1}{4} = 0.25 \text{ moles} $$

So, 10 g of gas X is equal to 0.25 moles.

Step 2: Calculate the molecular weight of gas X.

Molecular weight is defined as the mass per mole of a substance. We have the mass (10 g) and the number of moles (0.25 moles).

The formula for molecular weight is:

$$ \text{Molecular Weight} = \frac{\text{Mass}}{\text{Number of moles}} $$

Substituting the values:

$$ \text{Molecular Weight} = \frac{10 \text{ g}}{0.25 \text{ moles}} $$

To simplify the division, we can multiply the numerator and denominator by 4:

$$ \text{Molecular Weight} = \frac{10 \times 4}{0.25 \times 4} = \frac{40}{1} = 40 \text{ g/mol} $$

The molecular weight of gas X is 40 g/mol.

Summary of Calculation

The calculated molecular weight of gas X is 40.

Revision Table: Key Concepts

Additional Information: Ideal Gas Law

The relationship between pressure, volume, temperature, and the number of moles of an ideal gas is described by the Ideal Gas Law:

$$ PV = nRT $$

Where:

• P is pressure
• V is volume
• n is the number of moles
• R is the ideal gas constant (0.0821 L·atm/(mol·K) or 8.314 J/(mol·K))
• T is absolute temperature in Kelvin

At NTP (P = 1 atm, T = 273.15 K), the molar volume is:

$$ V/n = RT/P = (0.0821 \text{ L·atm/(mol·K)}) \times (273.15 \text{ K}) / (1 \text{ atm}) \approx 22.4 \text{ L/mol} $$

This confirms why 22.4 L/mol is used as the molar volume at NTP for calculating the number of moles.