The specific heat of solid copper is 0.385 J/g*C. What thermal energy change occurs when the temperature of a 40.10g sample of copper is cooled from 42.9C to 10.0C? Be sure to give you answer the proper sign.
I know this is part of the answer which
(42.9-10.0)*40.10*0.385=508 the second of the answer is where I am confused on
This is amount of heat is used to melt solid ice at 0.0C. The molar heat of fusion of ice is 6.00 kJ/mol. How many moles of ice are melted?
I use q = mass x specific heat x (Tfinal-Tinitial) which automatically takes care of the sign. Since the Cu is being cooled, it is giving off heat and that makes q negative. The problem states that proper sign should be used so I would make that -508 J.
mols ice x 6.00 kJ/mol = 0.508
Solve for mols ice.
To find the thermal energy change when the temperature of the copper sample is cooled, you need to use the formula:
Q = m * c * ΔT
where:
Q is the thermal energy change (in Joules),
m is the mass of the sample (in grams),
c is the specific heat of the substance (in J/g°C),
ΔT is the change in temperature (in °C).
Given:
m = 40.10 g
c = 0.385 J/g°C
ΔT = (42.9 - 10.0) °C = 32.9 °C
Plugging in the values, we have:
Q = 40.10 g * 0.385 J/g°C * 32.9 °C
Q = 508 J
Since the temperature is cooling (decreasing), the thermal energy change (Q) will be negative in this case. Therefore, the proper sign for the answer is -508 J.
Regarding the second part of your question, to determine the number of moles of ice melted, you can use the molar heat of fusion (ΔHf) and the equation:
Q = n * ΔHf
where:
Q is the thermal energy change (in Joules),
n is the number of moles of ice melted,
ΔHf is the molar heat of fusion (in J/mol).
Given:
Q = 508 J
ΔHf = 6.00 kJ/mol = 6000 J/mol (since 1 kJ = 1000 J)
Solving for n:
508 J = n * 6000 J/mol
n = 508 J / 6000 J/mol
n = 0.0847 mol
Therefore, 0.0847 moles of ice are melted.