Question

7.5 grams 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 respectively) (a) \(\mathrm{NO}\) (b) \(\mathrm{N}_{2} \mathrm{O}\) (c) \(\mathrm{CO}\) (d) \(\mathrm{CO}_{2}\)

Short answer

The gas is NO.

Step-by-step solution

Understand Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is defined as a temperature of 273.15 K (0°C) and a pressure of 1 atm. At STP, one mole of any ideal gas occupies 22.4 L.

Calculate Moles of Gas at STP

At STP, 22.4 L of any gas corresponds to 1 mole. Therefore, for 5.6 L:\[\text{moles} = \frac{5.6\, \text{L}}{22.4\, \text{L/mole}} = 0.25 \text{ moles}\]

Calculate Molar Mass of the Gas

The molar mass (M) can be found using the mass of the gas and the number of moles:\[M = \frac{\text{mass}}{\text{moles}} = \frac{7.5\, \text{g}}{0.25\, \text{moles}} = 30\, \text{g/mole}\]

Compare Molar Mass to Given Options

Compare the calculated molar mass of 30 g/mole with the molar mass of each gas option: - \( \text{NO} \): \( 14 + 16 = 30\, \text{g/mole} \) - \( \text{N}_2 \text{O} \): \( 2(14) + 16 = 44\, \text{g/mole} \) - \( \text{CO} \): \( 12 + 16 = 28\, \text{g/mole} \) - \( \text{CO}_2 \): \( 12 + 2(16) = 44\, \text{g/mole} \)The compound with a molar mass of 30 g/mole is \( \text{NO} \).

Key concepts

Molar Mass Calculations

Molar mass is the mass of one mole of a substance. It is expressed in units of grams per mole (g/mol). To calculate the molar mass of a compound, you sum up the atomic masses of all the atoms in its molecular formula. For example, to calculate the molar mass of nitric oxide (NO), you add the atomic mass of nitrogen (\[\text{N} = 14\, \text{g/mol} \]) and oxygen (\\(\text{O} = 16\, \text{g/mol}\)), resulting in \(30\, \text{g/mol}\).
The process involves a few steps:

• Identify the elements in the compound.
• Use the periodic table to find each element's atomic mass.
• Multiply the atomic mass by the number of times the element appears in the compound.
• Add the results together to get the total molar mass.

This calculation helps to understand how much one mole of that substance weighs, which is crucial in stoichiometry for relating the mass of a substance to the amount of substance present in moles.

Standard Temperature and Pressure

Standard Temperature and Pressure (STP) are conditions that are used as a reference point in chemistry to allow for comparison between different sets of data. At STP, the temperature is set to \(273.15\, \text{K}\) or \(0^{\circ}\text{C}\) and the pressure is \(1\, \text{atm}\). This standardization helps in predicting the behavior of gases.
One significant fact under STP is that one mole of an ideal gas will occupy exactly \(22.4\, \text{L}\) of space. This relationship makes it much simpler to calculate the number of moles given the volume of gas at STP, or vice versa, without needing additional conversions. In practical terms, if you have a sample of gas at STP, you can quickly determine the amount in moles based solely on its volume with the equation:\[\text{moles} = \frac{\text{volume of gas (L)}}{22.4}\]Understanding STP is essential for solving problems related to gas laws and for standardizing experimental measurements of gases.

Mole Concept

The mole is a fundamental unit in chemistry that provides a bridge between the atomic scale and the real-world scale. It is defined as exactly \(6.022 \times 10^{23}\) (Avogadro's number) of anything, usually atoms or molecules. This concept allows chemists to count particles by weighing them.
Using the mole concept, you can easily relate:

• Mass of a substance to the number of moles using the formula: \[\text{mass} = \text{moles} \times \text{molar mass}\]
• The number of particles to moles: \[\text{particles} = \text{moles} \times 6.022 \times 10^{23}\]

Understanding the mole concept is crucial for conversions in chemistry. It makes calculations manageable when dealing with the microscopic world of atoms and molecules, by allowing scientists to work with amounts of substances in the macroscopic world.