Question

(A): \(22.4 \mathrm{~L}\) of \(\mathrm{N}_{2}\) at NTP and \(5.6 \mathrm{~L} \mathrm{O}_{2}\) at NTP contain equal number of molecules. (R): Under similar conditions of temperature and pressure all gases contain equal number of molecules.

Short answer

Statement (A) is false; statement (R) is true.

Step-by-step solution

Understand the Concept

According to Avogadro's Law, equal volumes of gases at the same temperature and pressure contain an equal number of molecules. This means if two gases are measured under the same conditions, their volumes can be compared to determine the ratio of molecules.

Analyze Volume Data for Gases

We have \(22.4 \, \text{L}\) of \(\text{N}_2\) and \(5.6 \, \text{L}\) of \(\text{O}_2\) both at NTP. Compare these volumes directly, as they are under the same conditions. Avogadro's Law suggests equal volumes mean equal numbers of molecules.

Verify the Relationship Using Avogadro's Law

The total volume at NTP for \( \text{N}_2 \) is four times that of \( \text{O}_2 \), since \( 22.4 \, \text{L} \div 5.6 \, \text{L} = 4 \). Thus, \( \text{N}_2 \) has four times the number of molecules compared to \( \text{O}_2 \), contradicting point A.

Validate the Assertion and Reason

The assertion (A) is false, as the number of molecules in \( \text{N}_2 \) and \( \text{O}_2 \) are not equal given their volumes at NTP. The reason (R) is true because Avogadro's principle correctly states that under the same conditions, different gases have equal numbers of molecules in equal volumes.

Key concepts

NTP (Normal Temperature and Pressure)

Normal Temperature and Pressure, or NTP, is a standard set of conditions used to measure gases. NTP helps scientists and students compare gases easily by using a common frame of reference. It is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atmosphere (101.325 kPa).
These conditions are frequently used because they simplify calculations and allow for the comparison of different gases under equal conditions. At NTP, - measurements and observations are consistent. - volume calculations are straightforward. - comparisons between gases are direct and meaningful.
In practice, NTP is especially useful in exercises involving Avogadro's Law, where the behavior of gases is compared under consistent temperature and pressure.

molecular volume comparison

Comparing molecular volumes of gases is crucial when applying Avogadro's Law. According to this law, equal volumes of gases, when measured at the same temperature and pressure, contain an equal number of molecules. When dealing with problems involving gas volumes, this principle helps solve the exercises efficiently.
For example, if you have two different gases measured at NTP, you can directly compare the volumes to find out the ratio of molecules they contain. It's important to remember that the larger volume will naturally contain more molecules, provided both gases are under identical conditions. This concept lays the groundwork for understanding many scenarios where gases behave differently due to changes in their environmental conditions.

equal number of molecules in gases

Avogadro's Law asserts that under identical conditions of temperature and pressure, equal volumes of any gas will contain an equal number of molecules. This is a pivotal concept in chemistry that bridges the gap between the macroscopic world we observe and the microscopic world of molecules.
This point is significant in scenarios where gases are assumed to behave ideally. Ideal gas behavior allows scientists to predict and compare the amounts of substances in reactions by simply observing the volume ratios. Therefore, if we know that two gas samples are at NTP with equal volumes, we can immediately conclude they contain the same number of molecules.
This understanding assists in clarifying concepts like molar volumes and their applications in chemical equations and stoichiometry, ensuring accurate predictions of how gases will behave in various chemical reactions.