Question

In the gas equation \(P V=n R T\) the value of universal gas constant depends upon (1) The nature of the gas (2) The pressure of the gas (3) The temperature of the gas (4) The units of measurement

Short answer

The value of the universal gas constant depends on the units of measurement.

Step-by-step solution

- Understand the Universal Gas Constant

The universal gas constant, denoted as R, is a fundamental constant in chemistry and physics appearing in the ideal gas law.

- Analyze the Gas Equation

Observe the gas equation: \(PV = nRT\). Here, P stands for pressure, V for volume, n for the amount of substance (in moles), T for temperature, and R for the universal gas constant.

- Consider the Factors

The universal gas constant R is derived from physical constants specific to all ideal gases. It does not vary with the nature, pressure, or temperature of the gas.

- Determine the Dependency

The value of R can change based on the units used to measure pressure, volume, temperature, and amount of substance. Different unit systems require different numerical values for R.

- Conclude

Based on the analysis, the correct answer to the exercise is that the value of the universal gas constant depends on the units of measurement.

Key concepts

Ideal Gas Law

The ideal gas law is a fundamental equation in chemistry and physics. It illustrates the relationship between pressure, volume, temperature, and the number of gas particles. The equation is expressed as \(PV = nRT\). Here, **P** represents the pressure of the gas, **V** stands for its volume, **n** is the number of moles of the gas, **R** is the universal gas constant, and **T** is the temperature in Kelvin.

• This equation helps us understand how changing one of the four quantities affects the others in a contained gas system.
• It is derived based on the behavior of ideal gases, which are theoretical but provide close approximations to real gases under many conditions.

Understanding the ideal gas law is crucial for solving various problems related to gas behavior.

Units of Measurement

The universal gas constant, **R**, depends on the units used for measuring pressure, volume, and temperature. Common values for **R** include:

• 8.314 J/(mol·K) when pressure is in Pascals and volume in cubic meters.
• 0.0821 L·atm/(mol·K) when pressure is in atmospheres and volume in liters.

Changing the units of these quantities necessitates adjusting the value of R to maintain consistency. For example, if you switch from using atmospheres to Pascals for pressure, the value of **R** must adjust to reconcile this change. Selecting suitable units for your problem is essential to ensure correct calculations and interpretations.

Pressure and Volume Relationship

In the context of the ideal gas law, pressure and volume have an inverse relationship when temperature and the number of moles remain constant (Boyle’s Law). This means:

• If you increase the volume of a gas, the pressure decreases, assuming the temperature stays the same.
• Conversely, decreasing the volume increases the pressure.

This relationship is crucial for understanding how gases behave in different conditions, such as inside a balloon or a piston. For instance, compressing a gas into a smaller space increases its pressure, and understanding this helps with practical applications like designing pressure vessels and understanding respiratory mechanics.

Temperature Dependency

Temperature plays a significant role in the behavior of gases, as indicated by the ideal gas law. When the temperature increases:

• The kinetic energy of gas particles increases, causing them to move faster.
• This increased movement often results in increased pressure if the volume remains constant or expansion if the pressure is constant.

Conversely, lowering the temperature reduces the particles' kinetic energy, leading to lower pressure or contraction of volume. The direct relationship between temperature and pressure/volume underpins many real-world phenomena, such as how weather balloons expand as they ascend and enter lower pressure zones with decreasing temperatures. Always remember, temperature must be measured in Kelvin for these relationships to hold true in the ideal gas law.