Question

Which of the following statements about Avogadro's hypothesis is correct? (a) Under similar conditions of temperature and pressure, gases react with each other in simple ratio. (b) Under similar conditions of temperature and pressure, equal volumes of all gases contain same number of molecules. (c) At NTP all gases contain same number of molecules. (d) Gases always react with gases only at the given temperature and pressure.

Short answer

The correct statement about Avogadro's hypothesis is (b) Under similar conditions of temperature and pressure, equal volumes of all gases contain the same number of molecules.

Step-by-step solution

Understanding Avogadro's Hypothesis

Start by recalling Avogadro's hypothesis, which states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. This is a fundamental principle in chemistry that allows chemists to compare different gases under the same conditions.

Evaluating Statement (a)

Statement (a) mentions gases reacting in a simple ratio, which is related to the concept of stoichiometry in chemical reactions but does not provide information about the number of molecules. Therefore, this does not represent Avogadro's hypothesis.

Evaluating Statement (b)

Statement (b) directly aligns with Avogadro's hypothesis by saying that under similar conditions of temperature and pressure, equal volumes of all gases contain the same number of molecules. This option is consistent with Avogadro's hypothesis.

Evaluating Statement (c)

Statement (c) makes a specific mention of NTP (normal temperature and pressure), stating all gases contain the same number of molecules under these conditions. While this is true, it is just a specific application of the general theory expressed in statement (b), and hence is a correct implication of Avogadro's hypothesis.

Evaluating Statement (d)

Statement (d) suggests that gases always react with gases only at a given temperature and pressure which is not universally true and doesn't correlate with Avogadro's hypothesis. This statement is not correct regarding Avogadro's hypothesis.

Key concepts

Stoichiometry

Understanding stoichiometry is pivotal for mastering chemistry, especially when dealing with chemical reactions. Stoichiometry refers to the quantitative relationship between the reactants and products in a chemical reaction. It is based on the conservation of mass and the principle that substances react and form products in definite proportions.

For example, the reaction of hydrogen and oxygen to form water can be represented as \(2H_2 + O_2 \rightarrow 2H_2O\). This equation tells us that two moles of hydrogen react with one mole of oxygen to produce two moles of water. Using stoichiometry, we can predict the amount of reactants needed to form a certain amount of product, or vice versa. Even though Avogadro's hypothesis does not deal directly with the ratios of reactants and products, understanding the molar volumes of gases at a given temperature and pressure is crucial for stoichiometric calculations in reactions involving gases.

Chemical Reactions

Chemical reactions involve the transformation of one or more substances into new substances. The substances that undergo the reaction are known as reactants, and the new substances formed are called products. Chemical reactions are depicted by chemical equations, which show the reactants on the left side and the products on the right.

The coefficients in chemical equations represent the relative number of moles of each substance involved in the reaction and can be understood through the stoichiometry of the reaction. For reactions involving gases, Avogadro's hypothesis helps in simplifying the calculations, as it allows the assumption that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

Molar Volume

Molar volume is the volume occupied by one mole of a substance at a given temperature and pressure. For gases, the molar volume is especially important because gases are much more affected by changes in these conditions compared to solids or liquids.

Under the conditions of standard temperature and pressure (0°C and 1 atm), one mole of any ideal gas occupies 22.4 liters. This concept is a direct result of Avogadro's hypothesis and is essential for converting between moles and volume in gas stoichiometry. With this knowledge, you can easily calculate how many moles are in a given volume of gas or how much volume a certain number of moles will occupy at standard conditions.

Gases at NTP

Normal temperature and pressure (NTP), which is 0°C (273 K) and 1 atmosphere of pressure, is a standard set of conditions for the study of gases that simplifies comparison and calculations. At NTP, gases exhibit behavior that is close to that predicted by the ideal gas law, with Avogadro's hypothesis providing the groundwork.

According to Avogadro's hypothesis, at NTP, the molar volume of any ideal gas is 22.4 liters. This provides a useful base for conducting experiments and making predictions about gas reactions and properties. While answering questions related to Avogadro's hypothesis, it is crucial to differentiate between the general hypothesis and its application at NTP, which is just one specific scenario where the hypothesis holds true.