Math Problem Statement
The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 900 cubic centimeters left parenthesis cm cubed right parenthesis when the pressure is 200 millimeters of mercury (mm Hg), find the volume when the pressure is 400 mm Hg. Question content area bottom Part 1 When the pressure is 400 mm Hg, the volume is enter your response here ▼ mm Hg per cm cubed . mm Hg. cm cubed . cm cubed per mm Hg.
Solution
The relationship between the volume and pressure of a gas at a constant temperature follows Boyle's Law, which states that volume and pressure are inversely proportional. This can be written as:
or, equivalently,
where is a constant.
Step 1: Find the constant
We are given that the volume when the pressure . Using the equation :
Step 2: Use the constant to find the volume at
Now, using the same equation , we substitute and :
Solving for :
Final Answer:
When the pressure is , the volume is 450 cubic centimeters (cm³).
Would you like more details or further clarification on this?
Related Questions:
- What happens to the volume if the pressure doubles again to 800 mm Hg?
- Can this law be applied to non-ideal gases? If so, how?
- How does temperature affect the relationship between pressure and volume in gases?
- What are the conditions for Boyle's Law to hold true?
- What would happen to the volume if the pressure is reduced to 100 mm Hg?
Tip:
In inverse relationships like this, as one variable increases, the other decreases proportionally, making the constant very useful for calculations!
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Math Problem Analysis
Mathematical Concepts
Inverse Proportions
Gas Laws
Algebra
Formulas
V ∝ 1/P
V * P = k (Boyle's Law)
Theorems
Boyle's Law
Suitable Grade Level
Grades 9-12
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