Given:
V₂ = 580 cm³
T₂ = 98°C + 273 = 371 K
T₁ = 50°C + 273 = 323 K
Required:
V₁
Strategy:
This is a gas law problem. What gas law should we use?
Since the given quantities are volume and temperature, we will use Charles' law. According to this gas law, the volume occupied by a gas is directly proportional to its absolute temperature keeping the pressure and the amount of gas constant.
Caution: The temperature must be converted to kelvin. If the given temperature is in degree Celsius, add 273 or 273.15 to convert it to kelvin.
The formula used for Charles' law is
[tex]\boxed{\dfrac{V_{1}}{T_{1}} = \dfrac{V_{2}}{T_{2}}}[/tex]
where:
[tex]V_{1} = \text{initial volume}[/tex]
[tex]T_{1} = \text{initial temperature}[/tex]
[tex]V_{2} = \text{final volume}[/tex]
[tex]T_{2} = \text{final temperature}[/tex]
Solution:
Starting with the formula of Charles' law
[tex]\dfrac{V_{1}}{T_{1}} = \dfrac{V_{2}}{T_{2}}[/tex]
Multiplying both sides of the equation by T₁ to solve for V₁
[tex]V_{1} = V_{2} \times \dfrac{T_{1}}{T_{2}}[/tex]
Substituting the given values and solving for V₂
[tex]V_{1} = \text{580 cm}^{3} \times \dfrac{\text{323 K}}{\text{371 K}}[/tex]
Therefore, the initial volume is
[tex]\boxed{V_{1} = \text{505 cm}^{3}}[/tex]
Answer:
V₁ = 505 cm³
[tex]\\[/tex]
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