A
glass bottle full of mercury has a mass 500g.
35°C, 2.43g of mercury are
expelled.
Calculate the mass of
f mercury remaining in
the | bottle. (Cubic expansivity. of mercury . is
1.8×x10^-4 K^(-1), linear . expansivity of glass is
8.0×10^(-4)k^(-1)
A glassed bottle full of mecury has mass 500g. On been heated through 30°c, 2.43g of mecury is expelled calculate the mass expensivity of mecury is equal to 1.8*10 -4k-1 and linear expansivity =-8.0*10-6k-1
To calculate the mass of mercury remaining in the bottle, we need to consider the change in volume of both the mercury and the glass due to the change in temperature.
Step 1: Calculate the change in volume of the mercury.
The cubic expansivity of mercury is given as 1.8×10^-4 K^(-1).
The change in temperature is given as 35°C.
Using the formula for change in volume:
ΔV = V₀ × β × ΔT
Where:
ΔV = change in volume
V₀ = initial volume
β = cubic expansivity of mercury
ΔT = change in temperature
Since the mass of mercury expelled (Δm) is given as 2.43g, we can use the density of mercury (ρ = 13.6 g/cm³) to calculate the initial volume (V₀) of the mercury:
V₀ = Δm/ρ
Let's calculate V₀:
V₀ = 2.43g / 13.6 g/cm³
Step 2: Calculate the change in volume of the glass.
The linear expansivity of glass is given as 8.0×10^(-4) K^(-1).
Using the same formula as above, but with linear expansivity (α) instead of cubic expansivity (β), we can calculate the change in volume of the glass (ΔV_glass):
ΔV_glass = V_glass × α × ΔT
Step 3: Calculate the mass of mercury remaining in the bottle.
The total change in volume (ΔV_total) is the sum of the change in mercury volume (ΔV) and the change in glass volume (ΔV_glass).
ΔV_total = ΔV + ΔV_glass
The mass of mercury remaining (m_remaining) can be calculated using the total change in volume (ΔV_total) and the density of mercury (ρ):
m_remaining = ΔV_total × ρ
Let's now calculate the mass of mercury remaining:
1. Calculate the change in volume of the mercury:
ΔV = V₀ × β × ΔT
2. Calculate the initial volume of the mercury:
V₀ = Δm/ρ
3. Calculate the change in volume of the glass:
ΔV_glass = V_glass × α × ΔT
4. Calculate the total change in volume:
ΔV_total = ΔV + ΔV_glass
5. Calculate the mass of mercury remaining:
m_remaining = ΔV_total × ρ
To calculate the mass of mercury remaining in the bottle, we need to consider the change in volume of mercury and the change in volume of the glass bottle due to the temperature increase.
The change in volume of the mercury can be calculated using its cubic expansivity (β), which is given as 1.8×10^(-4) K^(-1). The change in volume of a substance can be calculated using the formula:
ΔV = β * V0 * ΔT
where ΔV is the change in volume, β is the expansivity coefficient, V0 is the initial volume, and ΔT is the change in temperature.
Given that 2.43 g of mercury is expelled and the density of mercury is known to be 13.6 g/cm³, we can calculate the initial volume of mercury (V0) expelled using the equation:
V0 = m / ρ
where m is the mass and ρ is the density.
V0 = 2.43 g / 13.6 g/cm³
Using the given values, we can find the initial volume of mercury.
V0 = 0.178676 cm³
Now let's calculate the change in volume of the mercury:
ΔV = (1.8×10^(-4) K^(-1)) * (0.178676 cm³) * (35 - 0) °C
ΔV = 1.125×10^(-4) cm³
Next, we need to calculate the change in volume of the glass bottle due to the temperature increase. The linear expansivity coefficient (α) of glass is given as 8.0×10^(-4) K^(-1). The change in volume of an object with the change in temperature can be calculated using the formula:
ΔV = α * V0 * ΔT
where ΔV is the change in volume, α is the expansivity coefficient, V0 is the initial volume, and ΔT is the change in temperature.
Since the initial volume of the glass bottle is not given, we cannot directly calculate the change in volume. However, for small changes in temperature, the change in volume is directly proportional to the initial volume of the object.
Therefore, we can assume that the change in volume of the glass bottle is also 1.125×10^(-4) cm³.
Finally, to calculate the mass of the remaining mercury, we need to subtract the change in volume of the mercury and the change in volume of the glass bottle from the initial volume of mercury.
The remaining volume of mercury can be calculated as:
V_remaining = V0 - ΔV
V_remaining = 0.178676 cm³ - 1.125×10^(-4) cm³
Now, to find the mass of the remaining mercury, we need to multiply the remaining volume of mercury by the density of mercury (13.6 g/cm³):
m_remaining = V_remaining * ρ
Finally, we can calculate the mass of the remaining mercury in grams (g).