Ross pours water at 6.0 C into a container with a pressure of 23. torr. He then boils the water to a temperature of 34 C. The volume changes to 18. mL and pressure to 78. torr. What was the initial volume of the water?
To find the initial volume of the water, we can use the combined gas law formula, which relates the initial volume, pressure, and temperature of a gas to its final volume, pressure, and temperature. The formula is:
(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂
where:
P₁ = initial pressure (23. torr)
V₁ = initial volume (unknown)
T₁ = initial temperature (6.0 C)
P₂ = final pressure (78. torr)
V₂ = final volume (18. mL)
T₂ = final temperature (34 C)
Let's plug in the values we have:
(23. torr * V₁) / (6.0 C) = (78. torr * 18. mL) / (34 C)
Now, let's simplify the equation:
23. * V₁ = (78. * 18.) * (6.0 / 34)
Rearranging the equation to solve for V₁:
V₁ = ((78. * 18.) * (6.0 / 34)) / 23.
Calculating the expression on the right side:
V₁ ≈ 20.781 mL
Therefore, the initial volume of the water was approximately 20.781 mL.