Main Concept

A common form of the Ideal Gas Law formula is $P V \= n R T$, where:

 - P is the absolute pressure, measured in pascals (denoted Pa).

 - V is the volume, measured in cubic meters $\left({\mathrm{m}}^3\right)$.

 - n is the number of moles of the gas, which is found using the equation $n\=\frac{m}{M}$ where $m$ is the mass and M is the molar mass.

 - R     is the ideal, or universal, gas constant and always takes on the value $8.314 \frac{J}{\mathrm{mol} K}$.

 - T is the temperature, measured in kelvin (K).

Since R is a constant, once you have values for three of the remaining four components, the fourth component can be computed using the formula. In the entry boxes below, you can enter values for the three of the following entities: absolute pressure (in pascals), volume (in liters), mass (in grams), and temperature (in degrees Celsius).  Once three values have been entered, the fourth will be computed automatically assuming that the gas is carbon dioxide (CO₂) which has a molar mass of 44.01 grams per mol. If the fourth entry does not compute automatically, either click outside the entry region or click 'Update Values'.

When all four entries have values in them, you can change any of those values manually, but be careful of which value is recalculated; this is controlled by the drop-down menu.

The Ideal Gas Law Challenge

If the absolute pressure is between 140 and 550 $\mathrm{kPa}$, the volume is between 10 and 50 $\mathrm{L}$, the mass is between 50 and 500 $\mathrm{g}$, and the temperature is between 17 and 22 $°\mathrm{C}$, an illustration of this scenario will be shown in the plot and gauges below. See if you can find a way to adjust the values so that the plot appears!

HINT

You may find it difficult to adjust the temperature, as small changes in absolute pressure, volume, and mass can cause apparently large relative changes to the temperature (as measured in degrees Celsius). This is because the 0 point on the Celsius temperature scale is shifted compared to the Kelvin scale which is part of the Ideal Gas Law:   TK = TC + 273.15.   For example a 3°C change seems like a 15% relative change when we think of a normal temperature being around 20°C, but it's actually a little over 1% on the Kelvin scale. To ensure that the temperature is within range to be plotted, first ensure that temperature is not selected in the drop-down menu.  Then, enter the temperature value manually, and adjust the other three using the controls until all of them are within range.

Temperature:  $°\mathrm{C}$

Absolute Pressure:  kPa$$

Quantity that will be computed:

        Absolute PressureVolumeMassTemperature         $$

Volume: L

Mass: g 

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