To solve the given question about the ideal gas constant [tex]\( R \)[/tex] in the Ideal Gas Law, we need to understand why [tex]\( R \)[/tex] has different values.
The Ideal Gas Law is given by:
[tex]\[ PV = nRT \][/tex]
Here:
- [tex]\( P \)[/tex] = Pressure
- [tex]\( V \)[/tex] = Volume
- [tex]\( n \)[/tex] = Number of moles
- [tex]\( R \)[/tex] = Ideal gas constant
- [tex]\( T \)[/tex] = Temperature
The value of [tex]\( R \)[/tex] is dependent on the units used for pressure ([tex]\( P \)[/tex]), volume ([tex]\( V \)[/tex]), and temperature ([tex]\( T \)[/tex]). Different units for these quantities necessitate different values of [tex]\( R \)[/tex] to keep the Ideal Gas Law valid.
1. Pressure can be measured in atmospheres (atm), pascals (Pa), or mmHg.
2. Volume can be measured in liters (L) or cubic meters (m³).
3. Temperature must always be in Kelvin (K) when using the Ideal Gas Law to ensure consistency.
4. Number of moles ([tex]\( n \)[/tex]) is a measure of the amount of substance and is expressed in moles (mol).
Given these variations, the ideal gas constant [tex]\( R \)[/tex] must adjust accordingly to maintain consistency in the equation. This means that different unit combinations will require different values of [tex]\( R \)[/tex].
The root cause of these differing values for [tex]\( R \)[/tex] is related to the units of measurement used for pressure, volume, and sometimes temperature. However, fundamentally, the value of [tex]\( R \)[/tex] changes because of the combination of these units.
Let’s break down the impact of each option provided:
- Pressure: Different units of pressure (atm, Pa, mmHg) change the value of [tex]\( R \)[/tex] when used in the equation.
- Temperature: Temperature in the Ideal Gas Law is always in Kelvin, so it doesn’t contribute to different values of [tex]\( R \)[/tex].
- Volume: Different units of volume (L, m³) impact the value of [tex]\( R \)[/tex].
- Moles: The amount in moles is consistent in the SI system and does not change [tex]\( R \)[/tex].
Therefore, considering that the problem inherently lies in the units used:
The quantity that causes the difference in the value of [tex]\( R \)[/tex] is fundamentally linked to units of measurement.
Since "units of measurement" is not one of the provided choices, we must understand which option closely correlates to this concept. Given that:
- The number of moles [tex]\( n \)[/tex] is a core aspect of the gas constant’s definition and the change in [tex]\( R \)[/tex] values can be seen as adjusting for a given amount of substance.
Thus, moles is the best choice among the provided options.
So, the correct answer is:
D. Moles
