Question

Explain the important distinctions between (a) barometer and manometer; (b) Celsius and Kelvin temperature; (c) ideal gas equation and general gas equation; (d) ideal gas and real gas.

Short answer

Barometers measure atmospheric pressure and manometers measure pressure of a gas in a closed system. Celsius is a relative temperature scale with the freezing and boiling points of water as reference, Kelvin is an absolute temperature scale starting at absolute zero. Ideal gas equation and general gas equation are expressions of state for gases, with the ideal gas equation applicable to nonexistent ideala gases and the general gas equation applicable to all cases. Ideal gases are hypothetical, non-interacting gases that perfectly fit the ideal gas equation. Real gases are actual gases that do not completely adhere to the ideal gas equation under certain conditions.

Step-by-step solution

Distinction between barometer and manometer

A barometer is a device designed to measure atmospheric pressure. This measurement is often used in weather forecasting and the study of how altitude affects pressure. A manometer, on the other hand, measures the pressure of a gas or usually a closed system and it's often used in laboratory settings to measure the pressure of gas samples.

Celsius and Kelvin temperature

Celsius is a unit of measurement for temperature where the freezing point of water is 0 degree and boiling point is 100 degrees at standard atmospheric pressure. Kelvin is the absolute temperature scale, a thermodynamic temperature scale where absolute zero, the lowest possible temperature, is 0 Kelvin. To convert from Celsius to Kelvin, add approximately 273.15 to the Celsius temperature.

Ideal gas equation and general gas equation

The ideal gas equation states that the product of the pressure and volume of an ideal gas is directly proportional to the absolute temperature. It is expressed as \(PV = nRT\), where n is the number of moles of gas, R is the universal gas constant, and T is the temperature in Kelvin. The general gas equation, on the other hand, expresses how pressure, volume and temperature interact in a gas sample when the amount of gas can change. It is expressed as \(P_1V_1/T_1 = P_2V_2/T_2\).

Ideal gas and real gas

An ideal gas is a hypothetical gas that perfectly fits into the equation \(PV = nRT\). This means that the gas particles do not interact and have zero volume. In reality, these assumptions are not completely true and hence the term Ideal Gas. A real gas is an actual existing gas that does not adhere to the ideal gas law under certain conditions. These gases show deviations from ideal behavior at high pressures and low temperatures due to the attractions between molecules and the volume occupied by gas molecules.

Key concepts

Barometer vs Manometer

The barometer and the manometer are both instruments used to measure pressure, but they differ in the type of pressure they measure and their applications.

A barometer is specifically designed to measure atmospheric pressure. This is the pressure exerted by the air in the Earth's atmosphere and is vital for weather forecasting. For instance, declining atmospheric pressure usually signals that stormy weather is approaching. Barometers often use mercury, and one classic type is the mercury barometer, where atmospheric pressure can be observed by the height of mercury within a tube.

On the other hand, the manometer measures the pressure of a gas within a closed system. It is widely used in laboratories and industries to measure pressure in systems containing gases. Manometers can come in different forms, such as the U-tube manometer and the digital manometer, and are crucial for processes where precise gas pressure readings are necessary. Unlike barometers, manometers can measure both positive and negative pressures relative to atmospheric pressure.

Celsius vs Kelvin

The Celsius and Kelvin scales are both used to measure temperature, but they are not interchangeable and serve slightly different purposes.

The Celsius scale sets the freezing point of water at 0 degrees and its boiling point at 100 degrees under standard atmospheric pressure. This makes it intuitive for everyday use and popular in most of the world for general temperature measurements.

Kelvin, on the other hand, is the preferred unit in the scientific community because it's an absolute temperature scale. It begins at absolute zero, which is the theoretical point where all molecular motion ceases. This leads to a simple and direct relation with the laws of thermodynamics. Absolute zero is 0 Kelvin, which is approximately -273.15 degrees Celsius. To convert degrees Celsius to Kelvin, one simply adds 273.15. This absolute nature of Kelvin makes it essential for scientific calculations involving temperature, such as those in gas laws.

Ideal Gas vs Real Gas

Understanding the differences between ideal and real gases is fundamental in chemistry, particularly when studying gases and their behaviors.

An ideal gas is a theoretical construct and follows the ideal gas law, expressed as \(PV = nRT\). This law assumes that gas molecules do not interact and occupy a negligible volume, meaning they neither attract nor repel each other, and each molecule is infinitely small. Under these conditions, a gas would behave perfectly according to the formula, without deviations.

However, real gases do not necessarily follow the ideal gas law under all conditions. At high pressures, the volume of the gas molecules becomes significant compared to the total volume of gas, leading to deviations. Similarly, at low temperatures, the interactions between molecules become significant. These factors cause real gases to deviate from ideal behavior, illustrating the limits of the ideal gas model. The van der Waals equation is often used to adjust the ideal gas law to account for these real gas behaviors.

Ideal Gas Equation

The ideal gas equation is a central concept in the study of gases and their behaviors under different conditions.

The equation is \(PV = nRT\), where:

• \(P\) stands for pressure
• \(V\) is the volume
• \(n\) represents the amount of gas in moles
• \(R\) is the universal gas constant
• \(T\) denotes temperature in Kelvin

This relationship shows that, for a fixed amount of gas, the product of pressure and volume is directly proportional to the temperature, given that the gas behaves ideally. This equation helps predict how a change in one variable (like volume) will affect another (like pressure), assuming temperature and moles of gas remain constant.

It is important, however, to understand the ideal gas equation as a simple model that provides a good approximation under many conditions, especially when those gases are at high temperatures and low pressures. Understanding when and how gases deviate from this equation is thus equally necessary for a deeper grasp of gas behaviors.