The ice skate of a 210-pound hockey player is in contact with the ice over a 2.5mm x 15cm area. Determine the freezing point of the ice under the blade of the skate?
To determine the freezing point of the ice under the blade of the skate, we need to use the concept of pressure and the freezing point depression equation.
The formula to calculate the freezing point depression is:
ΔT = Kf * m
where:
ΔT is the change in freezing point
Kf is the cryoscopic constant (a property of the solvent, in this case, water)
m is the molality of the solute (in this case, the hockey player's weight)
First, let's convert the given area to square meters:
2.5 mm * 15 cm = 0.025 m * 0.15 m = 0.00375 sq. m
Now, we need to calculate the pressure. Pressure is defined as force divided by area:
Pressure = player's weight / area
Weight = 210 pounds * 9.8 m/s^2 (acceleration due to gravity) = 2058 N
Area = 0.00375 sq. m
Pressure = 2058 N / 0.00375 sq. m = 548,800 Pa
Next, we need to convert the pressure into atmospheric pressure (which is the pressure at the freezing point of water). Atmospheric pressure is approximately 101,325 Pa.
ΔP = 548,800 Pa - 101,325 Pa = 447,475 Pa
Now, we can calculate the molality (m) of the solute using the equation:
m = ΔP / Kf
The cryoscopic constant (Kf) for water is approximately 1.86 °C/m.
m = 447,475 Pa / 1.86 °C/m = 240,588.7 °C/m
This value represents the molality of the solute. The molality is defined as the number of moles of solute per kilogram of solvent.
Finally, from the definition of molality, we can conclude that the change in freezing point (ΔT) is equal to the molality multiplied by the cryoscopic constant (Kf).
ΔT = m * Kf
ΔT = 240,588.7 °C/m * 1.86 °C/m = 447,469.74 °C
Therefore, the freezing point of the ice under the blade of the skate is approximately 447,469.74 °C below the normal freezing point of water.