The heat capacity of aluminum is 24.4 J/mol times degrees C. How much energy is released when 5.00 g Al is cooled from 50 degrees C to 30 degrees C.
a) 2440 J b) 90 J
c) 3.7 J d) 488 J
I said A, but the answer sheet says that the answer is B. Can someone please explain how this is so? I multiplied 5 times 24.4 times -20 (30-50) Thanks!
Never mind, I figured out I needed to convert the moles to grams and then I would use the q = mc delta t.
right
To find the amount of energy released when cooling aluminum from one temperature to another, we can use the formula:
∆Q = m * C * ∆T
Where:
∆Q represents the amount of energy released
m is the mass of aluminum (in grams)
C is the heat capacity of aluminum (in J/mol·°C)
∆T is the change in temperature (in °C)
Given:
m = 5.00 g
C = 24.4 J/mol·°C
∆T = 30 °C - 50 °C = -20 °C (since the temperature is decreasing)
Plugging in these values, we have:
∆Q = (5.00 g) * (24.4 J/mol·°C) * (-20 °C)
Here is where the discrepancy in your calculation lies. You multiplied the mass, heat capacity, and change in temperature correctly, but you forgot to convert the mass into moles. To convert grams to moles, we need to use the molar mass of aluminum. The molar mass of aluminum is approximately 26.98 g/mol.
To calculate the moles of aluminum:
moles = (mass of aluminum in grams) / (molar mass of aluminum)
= (5.00 g) / (26.98 g/mol)
≈ 0.185 mol
Now, we can calculate the energy released:
∆Q = (0.185 mol) * (24.4 J/mol·°C) * (-20 °C)
≈ -90 J
Since the energy is released, it has a negative sign. Therefore, the correct answer is b) 90 J.
It's important to keep in mind the units and conversions involved in the calculation to arrive at the correct answer.