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A 2.74-g sample of a substance suspected of being pure gold is warmed to 72.1 C and submerged into 15.2 g of water initially at 24.7 C. The final temperature of the mixture is 26.3 C. What is the heat capacity of the unknown substance? Could the substance be pure gold?
$$0.81 \mathrm{J} / \mathrm{g} \cdot^{0} \mathrm{C}$$
Chemistry 102
Chemistry 101
Chapter 9
Thermochemistry
Thermodynamics
Chemical reactions and Stoichiometry
Drexel University
University of Toronto
Lectures
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So in this problem, we're given the mass of a substance suspected of being pure gold and the temperature it starts at as well as the mass of the water it is submerged in. And the temperature of the water starts at as well as the equilibrium temperature. And we want to know if this substance is pure gold. And so how we do this is we can find these specific heat off the unknown substance. And if it matches the specific heat of gold, then we know we have pure gold. And so to do this, we use the formula. Q gained equals Q lost. We are then plug in the extended formula, which is mass one times the specific heat. One times the change in temperature of one equals the same for the second substance, and now we can plug in our values. So we have two point seven four grams of this unknown substance. We're looking for our C one and for a delta T one we know. The unknown substance starts at seventy two point one degrees Celsius and drops to twenty six point three degrees Celsius at equilibrium. And now we take the massive or water, fifteen point two grams times the specific heat of water, four point one eight times twenty six point three degrees Celsius. The equilibrium temperature minus the temperature of the water starts at which is twenty four point seven degrees Celsius. And so now, with all of this, we can solve for C one and when we do this, we get that C one is zero point eight one grams per jewel degrees Celsius. Now these specific heat of gold is equal to zero point one two nine grams per jewel degrees Celsius. And so we know that this unknown substance is not pure gold. And so this is our final answer for the calculated specific he capacity and because it does not match gold, we know that it is not pure goal.
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