Answered

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if a gas at 25.0°c occupies 3.60 l at a pressure of 1.00 atm what will be its volume at a pressure of 2.50 atm ​

Sagot :

Tokamakidn

Given:

[tex]P_{1} = \text{1.00 atm}[/tex]

[tex]V_{1} = \text{3.60 L}[/tex]

[tex]P_{2} = \text{2.50 atm}[/tex]

Required:

[tex]V_{2}[/tex]

Strategy:

This is a gas law problem. What gas law should we use?

Since the given quantities are pressure and volume, we will use Boyle's law. According to this gas law, the pressure of a gas is inversely proportional to its volume keeping the amount of gas and its temperature constant.

The formula used for Boyle's law is

[tex]\boxed{P_{1}V_{1} = P_{2}V_{2}}[/tex]

where:

[tex]P_{1} = \text{initial pressure}[/tex]

[tex]V_{1} = \text{initial volume}[/tex]

[tex]P_{2} = \text{final pressure}[/tex]

[tex]V_{2} = \text{final volume}[/tex]

Solution:

Starting with the formula of Boyle's law

[tex]P_{1}V_{1} = P_{2}V_{2}[/tex]

Dividing both sides of the equation by P₂ to solve for V₂

[tex]V_{2} = V_{1} \times \dfrac{P_{1}}{P_{2}}[/tex]

Substituting the given values and solving for V₂

[tex]V_{2} = \text{3.60 L} \times \dfrac{\text{1.00 atm}}{\text{2.50 atm}}[/tex]

Therefore, the final volume is

[tex]\boxed{V_{2} = \text{1.44 L}}[/tex]

Answer:

[tex]V_{2} = \text{1.44 L}[/tex]

[tex]\\[/tex]

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