Questions: Three samples of three different gases are listed in the table below. All the samples contain exactly 1 mole of gas and are at a temperature of 0.0°C. For each sample, decide whether the gas can be reasonably described as an ideal gas. If the gas isn't ideal, decide the most important reason why it isn't. sample pressure (atm) volume (L) ideal? If not ideal, the most important reason why not: --------------- A 1.9 15.0 yes There are attractions between the particles. The particles don't have zero volume. B 0.90 25.0 yes no There are attractions between the particles. The particles don't have zero volume.

Three samples of three different gases are listed in the table below. All the samples contain exactly 1 mole of gas and are at a temperature of 0.0°C.
For each sample, decide whether the gas can be reasonably described as an ideal gas. If the gas isn't ideal, decide the most important reason why it isn't.

sample  pressure (atm)  volume (L)  ideal?  If not ideal, the most important reason why not:
---------------
A  1.9  15.0  yes  There are attractions between the particles. The particles don't have zero volume.
B  0.90  25.0  yes  no
There are attractions between the particles. The particles don't have zero volume.
Transcript text: Three samples of three different gases are listed in the table below. All the samples contain exactly 1 mole of gas and are at a temperature of $0.0^{\circ} \mathrm{C}$. For each sample, decide whether the gas can be reasonably described as an ideal gas. If the gas isn't ideal, decide the most important reason why it isn't. $\left.\begin{array}{|c|c|c|c|c|}\hline \text { sample } & \begin{array}{c}\text { pressure } \\ (\mathrm{atm})\end{array} & \begin{array}{c}\text { volume } \\ \text { (L) }\end{array} & \text { ideal? } & \begin{array}{l}\text { If not ideal, the most } \\ \text { important reason why not: }\end{array} \\ \hline \text { A } & 1.9 & 15.0 & \text { yes } & \begin{array}{l}\text { There are attractions between the particles. } \\ \text { The particles don't have zero volume. }\end{array} \\ \hline \text { B } & 0.90 & 25.0 & \text { yes } & \text { no }\end{array} \begin{array}{l}\text { There are attractions between the particles. } \\ \text { The particles don't have zero volume. }\end{array}\right\}$
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Solution

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Solution Steps

Step 1: Determine if Sample A is an Ideal Gas

For Sample A, we need to check if the gas can be reasonably described as an ideal gas. The conditions given are:

  • Pressure: 1.9 atm
  • Volume: 15.0 L
  • Temperature: $0.0^{\circ} \mathrm{C}$ (273.15 K)

Using the ideal gas law: \[ PV = nRT \] where:

  • \( P \) is the pressure,
  • \( V \) is the volume,
  • \( n \) is the number of moles,
  • \( R \) is the ideal gas constant (0.0821 L·atm/(mol·K)),
  • \( T \) is the temperature in Kelvin.

Substituting the values: \[ (1.9 \, \text{atm}) (15.0 \, \text{L}) = (1 \, \text{mol}) (0.0821 \, \text{L·atm/(mol·K)}) (273.15 \, \text{K}) \]

Calculating the right-hand side: \[ 1 \times 0.0821 \times 273.15 = 22.41 \, \text{L·atm} \]

Comparing both sides: \[ 1.9 \times 15.0 = 28.5 \, \text{L·atm} \]

Since 28.5 L·atm is not close to 22.41 L·atm, Sample A does not behave as an ideal gas. The most important reason is likely due to the particles not having zero volume.

Step 2: Determine if Sample B is an Ideal Gas

For Sample B, the conditions are:

  • Pressure: 0.90 atm
  • Volume: 25.0 L
  • Temperature: $0.0^{\circ} \mathrm{C}$ (273.15 K)

Using the ideal gas law: \[ PV = nRT \]

Substituting the values: \[ (0.90 \, \text{atm}) (25.0 \, \text{L}) = (1 \, \text{mol}) (0.0821 \, \text{L·atm/(mol·K)}) (273.15 \, \text{K}) \]

Calculating the right-hand side: \[ 1 \times 0.0821 \times 273.15 = 22.41 \, \text{L·atm} \]

Comparing both sides: \[ 0.90 \times 25.0 = 22.5 \, \text{L·atm} \]

Since 22.5 L·atm is very close to 22.41 L·atm, Sample B can be reasonably described as an ideal gas.

Final Answer

\[ \begin{array}{|c|c|c|c|c|} \hline \text{sample} & \begin{array}{c}\text{pressure} \\ (\mathrm{atm})\end{array} & \begin{array}{c}\text{volume} \\ \text{(L)}\end{array} & \text{ideal?} & \begin{array}{l}\text{If not ideal, the most} \\ \text{important reason why not:}\end{array} \\ \hline \text{A} & 1.9 & 15.0 & \text{no} & \text{The particles don't have zero volume.} \\ \hline \text{B} & 0.90 & 25.0 & \text{yes} & \text{N/A} \\ \hline \end{array} \]

\(\boxed{\text{Sample A: no, The particles don't have zero volume.}}\)

\(\boxed{\text{Sample B: yes}}\)

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