Question

The volume of \(1.0 \mathrm{~g}\) of hydrogen in litres at NTP is: (a) \(22.4 \mathrm{~L}\) (b) \(1.12 \mathrm{~L}\) (c) \(11.2 \mathrm{~L}\) (d) \(44.56 \mathrm{~L}\)

Short answer

The volume of 1 gram of hydrogen at NTP is 11.2 L, answer (c).

Step-by-step solution

Understanding NTP

NTP stands for Normal Temperature and Pressure. At NTP, the conditions are defined as a temperature of 0°C (273.15 K) and a pressure of 1 atm.

Using Molar Volume Concept

At NTP, 1 mole of any ideal gas occupies a volume of 22.4 liters. This is an important principle to remember for calculations involving gases.

Calculating Moles of Hydrogen

To find out how many moles are present in 1 gram of hydrogen, use the molar mass of hydrogen, which is approximately 2 g/mol (since a hydrogen molecule is H₂). Thus, the number of moles is calculated as: \[ \text{Number of moles} = \frac{1.0 \text{ g}}{2 \text{ g/mol}} = 0.5 \text{ moles} \]

Determining Volume of Hydrogen Gas

Using the concept from Step 2, where 1 mole of hydrogen gas at NTP occupies 22.4 L, the volume for 0.5 moles can be calculated as: \[ \text{Volume} = 0.5 \text{ moles} \times 22.4 \text{ L/mole} = 11.2 \text{ L} \]

Choosing the Correct Answer

Based on the calculation, the volume of 1 gram of hydrogen at NTP is 11.2 liters. Therefore, the correct answer is (c) 11.2 L.

Key concepts

Molar Volume

The concept of molar volume is crucial when dealing with gases in chemistry. Molar volume refers to the volume occupied by one mole of any substance in its gaseous state. This is a consistent value when we're talking about ideal gases at specific conditions. For ideal gases at Normal Temperature and Pressure (NTP), which is a standard set of state conditions, the molar volume is always the same: 22.4 liters.
This figure is derived from the Ideal Gas Law, a fundamental principle in chemistry that connects pressure, volume, temperature, and moles of a gas through the equation: \( PV = nRT \). Here, \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is temperature.
Knowing that 22.4 liters is the volume one mole of any ideal gas occupies at NTP allows you to easily determine the volume that any given number of moles will occupy, simply by multiplying the number of moles by 22.4 L/mol. This property simplifies calculations in chemistry when working under these standard conditions.

NTP (Normal Temperature and Pressure)

NTP is an acronym for Normal Temperature and Pressure, which serves as a baseline to standardize measurements across laboratories worldwide. At NTP, the conditions are set at a temperature of 0°C (which is equivalent to 273.15 K) and a pressure of 1 atmosphere (atm). These conditions mirror those naturally found in some environmental zones on Earth, providing a realistic basis for many experiments and calculations relating to gases.
Under NTP conditions, the behavior of gases becomes particularly predictable. It's important to understand that these conditions are different from STP (Standard Temperature and Pressure), which may have slightly different parameters depending on the scientific context.

• 0°C means all thermodynamic calculations begin from this freezing point of water.
• 1 atm is a standard pressure, helping to ensure gas pressure is at a common baseline.

This makes NTP a very useful reference point when discussing molar volume and other gas-related properties, ensuring consistency and accuracy in experimental calculations.

Mole Concept

The mole concept is foundational in chemistry, providing a way to quantify atoms, molecules, and ions. A mole is defined as exactly 6.022 x 10²³ particles, known as Avogadro's number.
This large number is used because atoms and molecules are incredibly tiny. By using moles, chemists can work with manageable numbers instead of unwieldy quantities.
Moles link directly to the mass of a substance, as seen in the exercise where 1 gram of hydrogen is converted into moles using its molar mass. The molar mass is the mass of one mole of a substance expressed in grams per mole (g/mol). For hydrogen gas (H₂), the molar mass is about 2 g/mol because each hydrogen atom has an approximate mass of 1 u, and there are two atoms in a molecule of hydrogen gas. This makes conversions between mass and moles straightforward: you divide the mass of the substance by its molar mass.
With these conversions, you can then use other concepts like molar volume to find the properties of gases under certain conditions. Thus, the mole concept serves as a bridge connecting the atomic scale to the scale we experience daily.