Question

At 760 torr pressure and \(20^{\circ} \mathrm{C}\) temperature, \(1 \mathrm{~L}\) of water dissolves \(0.04 \mathrm{gm}\) of pure oxygen or \(0.02 \mathrm{gm}\) of pure nitrogen. Assuming that dry air is composed of \(20 \%\) oxygen and \(80 \%\) nitrogen (by volume). The masses (in \(\mathrm{g} / \mathrm{L}\) ) of oxygen and nitrogen dissolved by \(1 \mathrm{~L}\) of water at \(20^{\circ} \mathrm{C}\) exposed to air at a total pressure of 760 torr are respectively : (a) \(0.008,0.016\) (b) \(0.016,0.008\) (c) \(0.16,0.08\) (d) \(0.04,0.02\)

Short answer

The masses of oxygen and nitrogen dissolved in 1 L of water are respectively 0.008 gm and 0.016 gm.

Step-by-step solution

Determine the partial pressures

Calculate the partial pressure of oxygen and nitrogen using Dalton's Law of Partial Pressures. The total pressure is given as 760 torr. Since dry air is composed of 20% oxygen, the partial pressure of oxygen is 0.20 times the total pressure. For nitrogen, which makes up 80% of dry air, its partial pressure is 0.80 times the total pressure. For oxygen: Partial pressure = 0.20 * 760 torr = 152 torr. For nitrogen: Partial pressure = 0.80 * 760 torr = 608 torr.

Calculate the masses of gases dissolved

Use the given solubility data to determine how much oxygen and nitrogen dissolve at 760 torr and then adjust for their partial pressures. Since 1 L of water dissolves 0.04 gm of oxygen at 760 torr, at 152 torr (the partial pressure of oxygen), the dissolved oxygen would be (152/760) * 0.04 gm. Similarly, for nitrogen, use its partial pressure to find out how much would dissolve in 1 L of water: (608/760) * 0.02 gm.

Perform the calculations

For oxygen: Mass dissolved = (152/760) * 0.04 gm = 0.008 gm per 1 L of water. For nitrogen: Mass dissolved = (608/760) * 0.02 gm = 0.016 gm per 1 L of water.

Key concepts

Dalton's Law of Partial Pressures

Understanding Dalton's Law of Partial Pressures is essential when studying the behavior of gases, especially their solubility in liquids like water. In simple terms, this law states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases in the mixture. The partial pressure is the pressure that each gas would exert if it occupied the entire volume alone under the same conditions.

For example, if we have a container filled with a mixture of oxygen and nitrogen, Dalton's Law suggests we look at each gas separately. If oxygen constitutes 20% of the mixture and nitrogen 80%, the partial pressures are proportional to their volume percentages in relation to the total pressure. Hence, for a 760 torr total pressure scenario, the partial pressures calculated using Dalton's Law would be essential to solving solubility problems in physical chemistry.

Gases Solubility Calculations

The solubility of gases in water is a fundamental topic in chemistry, particularly when it comes to calculating how much gas dissolves in a liquid under specific conditions. The solubility is typically affected by factors like temperature, the nature of the gas, and importantly, the pressure of the gas above the liquid, a concept related to Henry's Law. To determine the mass of a gas that dissolves in water, chemists often use the given solubility data at a standard pressure, and then they apply ratios to find the solubility at a different partial pressure, as derived from Dalton's Law.

In practical problems, such as those for the Joint Entrance Examination (JEE) in physical chemistry, steps involve firstly determining the partial pressures of each gas, and then calculating the mass of gas dissolved using the proportional relationship between pressure and solubility. It's a straightforward calculation once we understand the concept that the amount of gas dissolved is directly proportional to its partial pressure over the liquid.

Physical Chemistry Problems JEE

Mastering physical chemistry problems is a crucial part of preparing for competitive exams like the Joint Entrance Examination (JEE), which is an engineering entrance assessment in India. Questions on the solubility of gases often feature in the exam and require a clear understanding of Dalton's Law of Partial Pressures as well as the principles governing gas solubility calculations.

Aspiring students should focus on mastering the relationship between the pressure of gases and their solubility in water—this involves consistent practice with a variety of problems to develop a strong foundation. Such exercises not only test the students' knowledge of scientific laws but also their problem-solving skills and their ability to apply theoretical concepts to practical scenarios.