I've seen the posts on solving this particular equation, and I know the answer is right in front of me. I'm still having trouble understanding why...
a 42g piece of ice at 0.0 degrees C is added to a sample of water at 7.8 degrees C. All the ice melts and the temperature decreases to 0.0 degrees C. How many grams of water are in the sample?
I feel really dumb for asking such an obvious question, but I think I'm over-thinking it... Thanks!
(mass ice x heat fusion) + (mass H2O x specific heat H2O x (Tfinal-Tinitial) = 0
Substitute and solve for mass H2O
Don't worry, it's completely normal to have trouble understanding certain concepts or equations. Let's break this down step by step.
To solve this problem, we need to use the heat transfer equation, which is:
Q = m * c * ΔT
where:
Q represents the heat transfer (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).
In this case, all the ice melts and its temperature increases from 0.0°C to 0.0°C (which means ΔT = 0). The water's temperature decreases from 7.8°C to 0.0°C (ΔT = -7.8°C).
Since the heat transferred to the ice equals the heat transferred from the water, we have:
Q(ice) = Q(water)
Using the equation for the heat transfer, we can write:
m(ice) * c(ice) * ΔT(ice) = m(water) * c(water) * ΔT(water)
Now, we know the mass and specific heat capacity of ice, as well as the specific heat capacity of water. We are trying to find the mass of water, so we can rearrange the equation:
m(water) = (m(ice) * c(ice) * ΔT(ice)) / (c(water) * ΔT(water))
Substituting the values:
m(water) = (42g * 2.09J/g°C * 0°C) / (4.18J/g°C * -7.8°C)
Now, we can calculate the mass of water:
m(water) = (0J) / (-32.604J)
Dividing by a negative value results in a positive value:
m(water) = 0g
Therefore, the mass of water in the sample is 0 grams.
It's important to note that in this particular scenario, the melting ice absorbed all the heat from the water, thus leaving no water in the sample. It's not a dumb question at all, and I hope this explanation helps clarify things for you!