If a container holds 0.865 L of ethyl alcohol at 12.0 degree{C}}, what is the volume of the alcohol when its temperature is raised to 35.0 degrees celcius?
i was thinking it was VT=VT and sub in but keep coming out with wrong answer
The V*T product is not constant. You may be thinking of gases, for which V/T is constant and a fixed pressure.
They are asking about liquid ethyl alcohol.
What you need is the coefficient of bulk (volume) thermal expansion of alcohol. It may be somewhere in your assignment, or in a chem/physics handbook you use, and it certainly can be found online. (It is about 10^-3 deg C^-1)
Multiply it by the temperature change (23 C) and the initial volyume to get the CHANGE in volume.
For further help, if needed, see
http://physics.info/expansion/
To solve this problem, we can use the equation for thermal expansion:
ΔV = V₀ * β * ΔT
where ΔV is the change in volume, V₀ is the initial volume, β is the coefficient of volume expansion, and ΔT is the change in temperature.
First, let's calculate the initial volume in meters cubed (m³) to match the units of the coefficient of volume expansion. We know that 1 L is equivalent to 0.001 m³. Therefore, the initial volume (V₀) can be converted as follows:
V₀ = 0.865 L * 0.001 m³/L = 0.000865 m³
Next, we need to determine the coefficient of volume expansion (β) for ethyl alcohol. The coefficient of volume expansion for most liquids is relatively constant and can be found by looking it up in a reference table. For ethyl alcohol, the coefficient of volume expansion is approximately 1.11 x 10⁻³ ºC⁻¹.
Now, we can calculate the change in volume (ΔV) by substituting the known values:
ΔV = 0.000865 m³ * (1.11 x 10⁻³ ºC⁻¹) * (35.0 ºC - 12.0 ºC)
ΔV = 0.000865 m³ * (1.11 x 10⁻³ ºC⁻¹) * (23.0 ºC)
ΔV ≈ 2.17 x 10⁻⁵ m³
Finally, we can calculate the final volume (Vf) by adding the change in volume to the initial volume:
Vf = V₀ + ΔV
Vf = 0.000865 m³ + 2.17 x 10⁻⁵ m³
Vf ≈ 0.000887 m³
To convert the volume back to liters, we multiply by 1000:
Vf ≈ 0.000887 m³ * 1000 L/m³ ≈ 0.887 L
Therefore, when the temperature is raised to 35.0 °C, the volume of the ethyl alcohol will be approximately 0.887 L.