Problem 94 - Chemistry

Question

At \(27^{\circ} \mathrm{C}, 10.0\) moles of a gas in a 1.50 -L container exert a pressure of 130 atm. Is this an ideal gas?

Step-by-Step Solution

Answer

The comparison of calculated R value with the standard Ideal Gas constant R will tell us if the gas behaves ideally or not. If the values match, the gas is ideal; if not, the gas is non-ideal.

Step 1: Convert Celsius to Kelvin

The question gives the temperature in Celsius, but for the Ideal Gas Law calculation, we have to convert the temperature to Kelvin. To do so, you add 273.15 to the Celsius temperature. In this case, converting 27 degrees Celsius to Kelvin is done by: 27 + 273.15 = 300.15 K.

Step 2: Calculate R using given data

Now we have to rearrange the Ideal Gas Law: \(PV=nRT\) to calculate the value of R. The rearrangement gives us: \(R = PV/nT\). Substituting P=130 atm, V=1.50 L, n=10.0 moles, and T=300.15 K, into the equation will give us: \(R = (130 * 1.50) / (10 * 300.15)\)

Step 3: Comparison with standard R

After we compute the value of R, we compare it with the known Ideal Gas constant R = 0.0821 L.atm/K.mol. If the values match (or the difference is negligible), the gas behaves ideally. If the calculation value of R is significantly different from standard R, the gas doesn't behave ideally.

Key Concepts

Gas Behavior

When we talk about gas behavior, we're discussing how gases interact within a container. Ideal gas behavior is a theoretical concept where gases perfectly adhere to the Ideal Gas Law, which states that \( PV = nRT \). In reality, gases occupy space and have intermolecular interactions, so their behavior can deviate from this model. However, under certain conditions - such as low pressure and high temperature - many gases exhibit nearly ideal behavior.In the exercise, we're examining if the gas in the container behaves ideally. We test this by comparing the calculated gas constant \((R)\) to the ideal gas constant. If they closely match, it indicates that the gas likely behaves similarly to an ideal gas. Otherwise, deviations might suggest real gas behavior influenced by interactions and volumes not accounted for in the ideal gas model.

Temperature Conversion

Temperature conversion is crucial when dealing with gas laws. Temperature directly affects gas behavior and must be in Kelvin for the Ideal Gas Law.The Kelvin scale starts at absolute zero, the point where molecular motion stops. When converting from Celsius to Kelvin, you add 273.15 to the Celsius value:

• This conversion aligns all temperatures to an absolute scale.
• Ensures consistency with the universal gas constant \(R\).

For example, in the problem, you start with a temperature of \(27^{\circ}C\). Converting this to Kelvin involves: \(27 + 273.15 = 300.15 \, K\). This is a crucial step because failing to convert to Kelvin leads to inaccurate results when applying the Ideal Gas Law.

Pressure Calculation

Pressure calculation is a vital aspect of understanding gas behavior. In the Ideal Gas Law, pressure \((P)\) is expressed in atmospheres (atm).Calculating "R" requires precise pressure inputs. Pressure reflects how forcefully gas molecules hit the walls of their container. Changes in pressure, along with temperature and volume, directly impact gas behavior. Using the exercise's data:

• Pressure = 130 atm
• This is used in the equation \(R = PV/nT\)

After the inputs are plugged in, checking how close our calculated "R" is to the standard \(R = 0.0821 \, L \cdot atm \/ K \cdot mol\) helps determine if the gas acts ideally. Thus, accurate pressure calculation is essential to validate the assumptions about gas behavior.