A 25g piece of an unknown metal alloy at 150 degrees Celsius is dropped into an insulated container with 200 g of ice. Calculate the specific heat capacity of the metal, given that 9.0 g of ice melted.
How would you work this out?
First you have to find the number of moles of water n=m/M = 9/18 = 0.05 mol
Latent heat of fusion of water is 6 kJ/mol, which means that 1 mole requires 6 kJ but you have only 0.05mol. Hence, the amount of energy required is 3kJ = 3000 J = q.
q(metal) = m*c*deltaT therefore c=q/mdeltaT=3000/(25*150)=0.80J/g0C
I hope it helps.
Cheers
JD (Chemistry tutor)
To calculate the specific heat capacity of the metal, you can follow these steps:
Step 1: Determine the amount of heat absorbed by the metal to raise its temperature from 150 degrees Celsius to its melting point.
To do this, we'll use the equation:
Q1 = m1 * c1 * ΔT1
Where:
Q1 = heat absorbed by the metal
m1 = mass of the metal (25 g)
c1 = specific heat capacity of the metal (unknown)
ΔT1 = change in temperature of the metal (melting point - initial temperature)
Since the metal is at 150 degrees Celsius, its melting point is most likely higher. Let's assume it is 1000 degrees Celsius, and calculate the heat absorbed by the metal:
ΔT1 = 1000°C - 150°C = 850°C
Step 2: Determine the amount of heat absorbed by the ice to raise its temperature from 0 degrees Celsius to its melting point (0 degrees Celsius).
To calculate this, we'll use the equation:
Q2 = m2 * c2 * ΔT2
Where:
Q2 = heat absorbed by the ice
m2 = mass of the ice (200 g - 9.0 g = 191 g)
c2 = specific heat capacity of ice (2.09 J/g °C)
ΔT2 = change in temperature of the ice (melting point - initial temperature)
Since the ice is at 0 degrees Celsius, we assume its melting point is also 0 degrees Celsius:
ΔT2 = 0°C - 0°C = 0°C
Step 3: Determine the amount of heat absorbed by the ice to melt completely.
To calculate this, we'll use the equation:
Q3 = m3 * ΔHf
Where:
Q3 = heat absorbed by the ice to melt completely
m3 = mass of the ice melted (9.0 g)
ΔHf = heat of fusion for ice (334 J/g)
Step 4: Calculate the total heat absorbed in the system.
The total heat absorbed is the sum of the three components calculated above:
Q_total = Q1 + Q2 + Q3
Step 5: Calculate the specific heat capacity of the metal.
The specific heat capacity of the metal (c1) can be calculated by rearranging the equation used in Step 1:
c1 = Q1 / (m1 * ΔT1)
Now, substitute the values into the equations and solve:
Q1 = m1 * c1 * ΔT1
Q1 = (25 g) * c1 * (850°C)
Q2 = m2 * c2 * ΔT2
Q2 = (191 g) * (2.09 J/g °C) * (0°C)
Q3 = m3 * ΔHf
Q3 = (9.0 g) * (334 J/g)
Q_total = Q1 + Q2 + Q3
Using the calculated values, substitute them into Q_total and solve for c1:
Q_total = Q1 + Q2 + Q3
Q_total = (25 g) * c1 * (850°C) + (191 g) * (2.09 J/g °C) * (0°C) + (9.0 g) * (334 J/g)
Finally, solve for c1:
c1 = Q1 / (m1 * ΔT1)
This calculation will give you the specific heat capacity of the metal.
To calculate the specific heat capacity of the unknown metal alloy, you need to use the formula:
q = m * c * ΔT
Where:
q is the heat transferred (in Joules),
m is the mass of the substance (in grams),
c is the specific heat capacity (in J/g°C), and
ΔT is the change in temperature (in °C).
First, let's determine the heat transferred to melt the ice. We know that 9.0 g of ice melted, so we need to calculate the heat required to melt it. The heat transferred for the phase change (from solid to liquid) is given by:
q = m * ΔH
Where ΔH is the heat of fusion of ice, which is 333.5 J/g.
q = 9.0 g * 333.5 J/g
q = 3001.5 J
Next, let's calculate the heat lost by the metal alloy. The heat lost equals the heat gained by the ice, which is calculated as follows:
q = m * c * ΔT
Here, the mass is given as 25 g, the specific heat capacity of water (ice) is 4.18 J/g°C, and the change in temperature (ΔT) is the final temperature of the mixture (0°C) minus the initial temperature of the metal alloy (150°C).
q = 25 g * 4.18 J/g°C * (0°C - 150°C)
q = -19,725 J
Since heat is transferred from the higher-temperature system to the lower-temperature system (in this case, from the metal to the ice), the heat value obtained is negative.
Finally, we can calculate the specific heat capacity (c) by rearranging the equation:
c = q / (m * ΔT)
c = -19,725 J / (25 g * (0°C - 150°C))
c ≈ 0.53 J/g°C
Therefore, the specific heat capacity of the unknown metal alloy is approximately 0.53 J/g°C.
heat lost by metal + heat gained by ice = 0
[mass metal x sp.h. x (Tfinal-Tinitial)] + [mass ice x heat fusiion)] = 0
25*X*(0-150) + (9g*333.5 J/g) = 0
Solve for X