kess473629
Answered

Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Which equation agrees with the ideal gas law?

A. [tex]\(\frac{V_1}{V_2} = \frac{V_1}{V_2}\)[/tex]
B. [tex]\(P_1 = P_2\)[/tex]
C. [tex]\(\frac{P_1 T_2}{P_2 T_1} = 1\)[/tex]

Sagot :

GinnyAnswer
To determine which equation agrees with the ideal gas law, let’s analyze each option step by step in accordance with the ideal gas law, which is expressed as:

[tex]\[ PV = nRT \][/tex]

where [tex]\( P \)[/tex] stands for pressure, [tex]\( V \)[/tex] for volume, [tex]\( n \)[/tex] for the number of moles of the gas, [tex]\( R \)[/tex] for the universal gas constant, and [tex]\( T \)[/tex] for temperature.

Given three choices:

1. [tex]\( V₁ = V₂ \)[/tex]
2. [tex]\( P₁ = P₂ \)[/tex]
3. [tex]\( \frac{P₁}{T₁} = \frac{P₂}{T₂} \)[/tex]

We will assess whether each equation aligns with the ideal gas law principles.

### Option 1: [tex]\( V₁ = V₂ \)[/tex]
This equation states that the volumes [tex]\( V₁ \)[/tex] and [tex]\( V₂ \)[/tex] are equal. However, this doesn’t directly relate to the pressure or temperature variables. Given the ideal gas law [tex]\( PV = nRT \)[/tex], volume could only be constant if the product of the pressure and the temperature (assuming the number of moles and gas constant remain unchanged) remains equivalent, but this option alone doesn’t encompass the relationship needed.

### Option 2: [tex]\( P₁ = P₂ \)[/tex]
This equation implies that the pressures [tex]\( P₁ \)[/tex] and [tex]\( P₂ \)[/tex] are equal. Similar to option 1, this does not account for the potential variation in volumes or temperatures. According to [tex]\( PV = nRT \)[/tex], pressure can stay constant only if a balance is maintained with changes in volume and temperature, but this agreement alone is insufficient for ideal gas behavior explanation.

### Option 3: [tex]\( \frac{P₁}{T₁} = \frac{P₂}{T₂} \)[/tex]
This equation can be rearranged for clarity to [tex]\( P₁ T₂ = P₂ T₁ \)[/tex]. This equation indicates that the pressures and temperatures of two states of the gas are related proportionally, which makes more sense in the context of the ideal gas law because it inherently considers alternate scenarios with pressures and temperatures, holding volume and the number of moles constant.

Therefore, the option that reflects the correct proportional relationship according to the ideal gas law is:

[tex]\[ \frac{P₁}{T₁} = \frac{P₂}{T₂} \][/tex]

Thus, the correct equation that agrees with the ideal gas law is:

[tex]\[ \boxed{3} \][/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.