Open Question
Which assumptions of the kinetic–molecular theory explain the behavior of gases described by Gay-Lussac's law? Explain your answer.
8. Gases, Liquids and Solids
Chemistry Gas Laws
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A 10.0 L cylinder with a movable piston exerts 3.00 atm of pressure. What will happen to the pressure if the volume of the container increases to 20.0 L?
a) It will double
b) It will decrease by half
c) It will increase slightly
d) No change
A
It will double
B
It will decrease by half
C
It will increase slightly
D
No change
Verified step by step guidance1
Identify the relationship between pressure and volume in a gas. This is described by Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when temperature and amount of gas are held constant.
Write down Boyle's Law equation: \( P_1 V_1 = P_2 V_2 \), where \( P_1 \) and \( V_1 \) are the initial pressure and volume, and \( P_2 \) and \( V_2 \) are the final pressure and volume.
Substitute the known values into the equation: \( 3.00 \, \text{atm} \times 10.0 \, \text{L} = P_2 \times 20.0 \, \text{L} \).
Solve for \( P_2 \) by rearranging the equation: \( P_2 = \frac{3.00 \, \text{atm} \times 10.0 \, \text{L}}{20.0 \, \text{L}} \).
Interpret the result: Since the volume doubles, the pressure will decrease by half, according to the inverse relationship described by Boyle's Law.
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