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.
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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.

The relationship between the volume \(V\) and pressure \(P\) 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:

\[
V \propto \frac{1}{P}
\]

or, equivalently,

\[
V \cdot P = k
\]

where \(k\) is a constant.

### Step 1: Find the constant \(k\)

We are given that the volume \(V = 900 \, \text{cm}^3\) when the pressure \(P = 200 \, \text{mm Hg}\). Using the equation \(V \cdot P = k\):

\[
900 \cdot 200 = k
\]

\[
k = 180,000
\]

### Step 2: Use the constant \(k\) to find the volume at \(P = 400 \, \text{mm Hg}\)

Now, using the same equation \(V \cdot P = k\), we substitute \(P = 400 \, \text{mm Hg}\) and \(k = 180,000\):

\[
V \cdot 400 = 180,000
\]

Solving for \(V\):

\[
V = \frac{180,000}{400} = 450 \, \text{cm}^3
\]

### Final Answer:

When the pressure is \(400 \, \text{mm Hg}\), the volume is **450 cubic centimeters (cm³)**.

Would you like more details or further clarification on this?

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### Related Questions:
1. What happens to the volume if the pressure doubles again to 800 mm Hg?
2. Can this law be applied to non-ideal gases? If so, how?
3. How does temperature affect the relationship between pressure and volume in gases?
4. What are the conditions for Boyle's Law to hold true?
5. 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!

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 (cm³) when the pressure is 200 millimeters of mercury (mm Hg), find the volume when the pressure is 400 mm Hg.

This problem uses Boyle's Law to find the volume of gas in a closed container as pressure increases. Learn how the volume of 900 cm³ at 200 mm Hg changes to 450 cm³ when the pressure rises to 400 mm Hg. Suitable for high school students learning about inverse proportions and gas laws.

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