Question

\(7.5 \mathrm{~g}\) of gas occupy \(5.6\) litres of volume at STP. The gas is (Atomic weight of \(\mathrm{C}, \mathrm{N}\), and \(\mathrm{O}\) are 12,14 and \(16 \mathrm{re}-\) spectively): (a) \(\mathrm{NO}\) (b) \(\mathrm{N}_{2} \mathrm{O}\) (c) CO (d) \(\mathrm{CO}_{2}\)

Short answer

The gas is NO.

Step-by-step solution

Determine Molar Volume at STP

At standard temperature and pressure (STP), 1 mole of any ideal gas occupies a volume of 22.4 litres. This is a constant used for gas calculations under these conditions.

Calculate Moles of Gas

Given that the gas occupies 5.6 litres at STP, we calculate the moles of gas using the molar volume. \[\text{Moles of gas} = \frac{\text{Volume}}{\text{Molar Volume at STP}} = \frac{5.6 \text{ L}}{22.4 \text{ L/mol}} = 0.25 \text{ mol}\]

Calculate Molar Mass of the Gas

With 7.5 grams of gas corresponding to 0.25 moles, calculate the molar mass (grams per mole) of the gas:\[\text{Molar mass} = \frac{\text{Mass}}{\text{Moles}} = \frac{7.5 \text{ g}}{0.25 \text{ mol}} = 30 \text{ g/mol}\]

Identify the Gas Based on Molar Mass

Compare the calculated molar mass with the options provided:- For NO, the molar mass is \(14 + 16 = 30 \text{ g/mol}\).- For other options: - \(\text{N}_2\text{O}\) (44 g/mol) - CO (28 g/mol) - \(\text{CO}_2\) (44 g/mol)The gas with a molar mass of 30 g/mol is NO.

Key concepts

Molar Volume at STP

To start, understanding the concept of molar volume at standard temperature and pressure (STP) is crucial. At STP, the temperature is set at 273.15 K (or 0°C) and the pressure is 1 atm (atmosphere). Under these conditions, one mole of an ideal gas occupies a volume of 22.4 liters. This value is a convenient constant for calculations involving gases in many chemistry problems.
The idea of molar volume primarily helps relate the amount of gas (in moles) to the volume it occupies at STP. This ensures consistency when solving problems, as we have a reference point to use.
For instance, if we know a gas occupies 5.6 liters at STP, we can use the formula: \[\text{Moles of gas} = \frac{\text{Volume}}{\text{Molar Volume at STP}}\] to find out how many moles of the gas we are dealing with. In this case, it works out to be 0.25 moles.

Molar Mass Determination

Once we know how many moles of a gas we have, the next step is determining the molar mass. Molar mass is the mass of one mole of a substance, commonly expressed in grams per mole (g/mol).
To determine the molar mass, we use this formula: \[\text{Molar mass} = \frac{\text{Mass}}{\text{Moles}}\] For example, if we have 7.5 grams of a gas and it consists of 0.25 moles, the molar mass is 30 g/mol. This means each mole of the gas weighs 30 grams.
Understanding molar mass is essential as it gives us insight into the weight of one mole of a particular gas, which is necessary for identifying gases and understanding their properties.

Identifying Gases by Molar Mass

Identifying gases through their molar mass involves comparing calculated values with known values of common gases. In the exercise given, we calculated the molar mass to be 30 g/mol.
The next step involves matching this calculated molar mass with the potential candidates provided in the options:

• NO (Nitric Oxide) = 14 (N) + 16 (O) = 30 g/mol
• \(\text{N}_2\text{O}\) = 44 g/mol
• CO (Carbon Monoxide) = 12 (C) + 16 (O) = 28 g/mol
• \(\text{CO}_2\) = 44 g/mol

Among the available options, only NO has a molar mass of 30 g/mol, making it the correct identity of the gas.
Recognizing gases by their molar mass is a fundamental skill in chemistry, allowing us to understand the composition and hypothesize reactions that these gases may partake in.