Solution Found!
In A, the picture depicts a cylinder with 0.1 mol of a gas
Chapter 6, Problem 99P(choose chapter or problem)
Cylinder Ain the picture below contains \(0.1 mol\) of a gas that behaves ideally. Choose the cylinder (B, C, or D) that correctly represents the volume of the gas after each of the following
changes. If none of the cylinders is correct, specify “none.”
(a) P is doubled at fixed n and T.
(b) T is reduced from \(400 K to 200 K\) at fixed n and P.
(c) T is increased from \(100^{\circ} \mathrm{C}\) to \(200^{\circ} \mathrm{C}\) at fixed n and P.
(d) \(0.1 mol\) of gas is added at fixed P and T.
(e) \(0.1 mol\) of gas is added and P is doubled at fixed T.
Equation Transcription:
100°C
200°C
Text Transcription:
0.1 mol
400 K to 200 K
100°C
200°C
Questions & Answers
QUESTION:
Cylinder Ain the picture below contains \(0.1 mol\) of a gas that behaves ideally. Choose the cylinder (B, C, or D) that correctly represents the volume of the gas after each of the following
changes. If none of the cylinders is correct, specify “none.”
(a) P is doubled at fixed n and T.
(b) T is reduced from \(400 K to 200 K\) at fixed n and P.
(c) T is increased from \(100^{\circ} \mathrm{C}\) to \(200^{\circ} \mathrm{C}\) at fixed n and P.
(d) \(0.1 mol\) of gas is added at fixed P and T.
(e) \(0.1 mol\) of gas is added and P is doubled at fixed T.
Equation Transcription:
100°C
200°C
Text Transcription:
0.1 mol
400 K to 200 K
100°C
200°C
ANSWER:
Solution 99P:
Step 1: (a) P is doubled at fixed n and T.
Here, we are going to find out the correct cylinder which represent the volume of the gas when
P is doubled at fixed n and T.
We know, from the ideal gas equation
-----(1)
Where, P is the pressure
T is the temperature
R is the gas constant
V is the volume of the gas
When P is doubled at constant T and n
Volume of the gas will be
Pressure of the gas = 2P
Therefore, the equation (1) will be
= nRT----(2)
Therefore, dividing the equation (2) by (1) we get
=
= 1
V
Therefore, when the P is doubled at constant T and n, the volume of gas will be ½ th to the original or initial volume of the gas.
Therefore, the cylinder B is the best or correct representation of the condition(a).