A gas mixture contains 75.2% nitrogen and 24.8% krypton by mass. What is the partial pressure of krypton in the mixture if the total pressure is 745 mmHg?

Understanding Dalton's Law of Partial Pressures is pivotal when analyzing a gas mixture. This fundamental law states that the total pressure exerted by a mixture of non-reactive gases is equal to the sum of the partial pressures of each individual gas in the mixture. In simpler terms, if you have a collection of gases in a container, each gas behaves as if it's the only one present and contributes to the overall pressure independent of the other gases.

As an analogy, imagine if you and your friends put money into a piggy bank. Dalton's Law suggests that the total amount of money in the bank is simply the sum of each person's contribution. When applied to our exercise, we'll use Dalton's Law to pinpoint the pressure solely attributable to krypton (\( P_{Kr} \) ) by using its mass percentage in the gas mixture and the total pressure provided.

The concept of mass percentage is crucial in chemistry. It indicates how much of a certain component (in mass) is present in a mixture or solution compared to the total mass. It's calculated by taking the mass of the component of interest, dividing it by the total mass of the mixture, and then multiplying by 100 to get a percentage. This allows chemists to describe the concentration of components in a mixture in a clear and understandable way.

In our exercise, krypton's mass percentage is given as 24.8%. This value reflects that if you had 100 grams of the gas mixture, 24.8 grams would be krypton. These mass-based measurements are particularly useful when calculating partial pressures of gases, as we connect the mass of each gas to its individual pressure contribution.

Significant figures are a way to express precision in measurements. They include all the certain digits and the first uncertain digit in a number. The rules for significant figures help ensure that calculations and results reflect the inherent precision of the measurements involved. For example, if a scale can measure to the nearest gram, then a weight of 130 grams has two significant figures because the '3' is certain and the '0' indicates the scale's limit of precision.

In the context of the exercise provided, significant figures play a role when calculating the partial pressure of krypton. The rule is to express the answer with the same number of significant figures as the least precise measurement you started with. Since 24.8% and 745 mmHg both have three significant figures, the final answer for the partial pressure of krypton should also be rounded to three significant figures to adequately represent the precision of the given data.

The composition of a gas mixture can be described in terms of either mole fraction or mass percentage. Mole fraction is the ratio of the number of moles of a particular component to the total moles of all components in the mixture. Mass percentage, as used in our exercise, represents the ratio of the mass of a specific gas to the total mass of the mixture. It is important to convert this percentage to a decimal (i.e., 24.8% becomes 0.248) when using it in calculations.

In regards to partial pressures, knowing the composition of a gas mixture allows us to apply Dalton's Law and calculate the pressure that each component exerts separately. This is highly valuable in various applications such as industrial gas production, anesthetics in medicine, and diving where the correct mixture of breathable air is critical for human safety.