A sample of iron was heated to 161.0°C, then placed into 338 g of water at 21.6°C. The temperature of the water rose to 26.9°C. How many grams of iron were in the sample?
Specific heat for Iron is 0.473.
You have no units on the specific heat of Fe.
heat lost by Fe + heat gained by water = 0
[mass Fe x specific heat Fe x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Substitute the numbers and solve for mass Fe.
To determine the number of grams of iron in the sample, we need to use the equation for heat transfer:
q = mcΔT
where:
q = heat transferred (in Joules)
m = mass of the substance (in grams)
c = specific heat capacity of the substance (in J/g°C)
ΔT = change in temperature (in °C)
In this case, we need to calculate the mass of iron (m), so we rearrange the equation:
m = q / (cΔT)
First, let's calculate the heat transferred (q) using the equation:
q = mwater * cwater * ΔTwater
where:
mwater = mass of water = 338 g
cwater = specific heat capacity of water = 4.184 J/g°C (rounded value)
ΔTwater = change in temperature of water = 26.9°C - 21.6°C = 5.3°C
Substituting the values into the equation:
q = 338 g * 4.184 J/g°C * 5.3°C
Now, we need to calculate the heat transferred by the iron to the water. The heat transferred by the iron is equal to the heat gained by the water:
qiron = - qwater
Since q = mcΔT, we can rewrite it as:
qiron = miron * ciron * ΔTiron
where:
ciron = specific heat capacity of iron = 0.473 J/g°C (given)
ΔTiron = change in temperature of iron = 26.9°C - 161.0°C (negative, since the iron loses heat in this case)
Substituting the values into the equation:
miron * 0.473 J/g°C * (-134.1°C) = - mwater * 4.184 J/g°C * 5.3°C
Simplifying the equation:
miron = - (mw * cw * ΔTw) / (ciron * ΔTiron)
First, we calculate the right-hand side (RHS) of the equation:
RHS = - (338 g * 4.184 J/g°C * 5.3°C) / (0.473 J/g°C * (-134.1°C))
Finally, calculate the value of miron by taking the absolute value of the right-hand side:
miron = abs(RHS)
After performing the calculations, you'll find the number of grams of iron in the sample.