It is observed that 55.50 mL of water at 20 ∘C completely fills a container to the brim. When the container and the water are heated to 60 ∘C, 0.37 g of water is lost. Density of water at 60 ∘C is 0.98324 g/mL.
What is the coefficient of volume expansion of the container?
The coefficient of volume expansion of the container is 0.0067 K^-1.
To find the coefficient of volume expansion of the container, we need to understand the relationship between temperature and volume.
The coefficient of volume expansion (β) is a property that quantifies how much a substance expands or contracts with a change in temperature. It is given by the equation:
β = (1/V)(ΔV/ΔT)
where V is the initial volume, ΔV is the change in volume, and ΔT is the change in temperature.
In this case, we know that the initial volume (V) of the container is 55.50 mL at 20 ∘C. The change in volume (ΔV) can be determined by the amount of water lost when heated to 60 ∘C. And the change in temperature (ΔT) is the difference between the two temperatures (60 ∘C - 20 ∘C).
Let's calculate the change in volume (ΔV) first:
ΔV = Mass lost / Density at 60 ∘C
Given that 0.37 g of water is lost and the density of water at 60 ∘C is 0.98324 g/mL, we can substitute the values:
ΔV = 0.37 g / 0.98324 g/mL
Now, let's calculate ΔT:
ΔT = 60 ∘C - 20 ∘C
Now that we have both ΔV and ΔT, we can calculate the coefficient of volume expansion (β):
β = (1/V)(ΔV/ΔT) = (1/55.50 mL)(0.37 g / 0.98324 g/mL)/(60 ∘C - 20 ∘C)
Simplifying the expression further will give you the coefficient of volume expansion of the container.
To find the coefficient of volume expansion of the container, we can use the formula:
ΔV = β * Vi * ΔT
where:
ΔV is the change in volume of the container
β is the coefficient of volume expansion of the container
Vi is the initial volume of the container
ΔT is the change in temperature
In this case:
ΔV = -0.37 g / (0.98324 g/mL) = -0.376 mL (note: negative sign indicates a decrease in volume)
Vi = 55.50 mL
ΔT = 60 °C - 20 °C = 40 °C
Now we can substitute these values into the formula and solve for β:
-0.376 mL = β * 55.50 mL * 40 °C
β = -0.376 mL / (55.50 mL * 40 °C)
Simplifying the expression:
β ≈ -0.000214 mL / (mL * °C)
Therefore, the coefficient of volume expansion of the container is approximately -0.000214 mL / (mL * °C).