Chemistry: 2 samples of the same liquid but different temp - final temp?

In summary, the final temperature of a mixture of 75 mL of pure liquid at 245 K and 100 mL of pure liquid at 365 K is 314 K.
  • #1
meganw
97
0

Homework Statement



75 mL of a pure liquid at 245 K is mixed with 100 mL of the same pure liquid 365 K. What is the final temperature?

The answer is 314 K but I'm not sure why!

Thank you! =)

Homework Equations



It says this problem has to do with Calorimetry but I'm not sure why! Calorimentry equations involve q=mc(d)t...but how would you incorporate both liquids?

The Attempt at a Solution



q=mc(d)t? I'm so lost, sorry!
 
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  • #2
Yes you need that equation. Energy is conserved. You need to remember that the heat lost by the water at 365 K is equal to the heat gained by the volume of water at 345 K.
 
  • #3
I'm sorry I'm afraid I still don't understand...how can I use q=mcat for this problem?
 
  • #4
That equation tells you the amount of thermal energy that is transferred between a mass m and its surroundings to undergo a temperature change ∆T.

So, you have Q1 = m1c∆T for the first volume of water, and Q2 = m2c∆T for the second volume of water.
When they are mixed, the heat lost by the water at the higher temperature will equal the heat gained by the water at the lower temperature. They will come to equilibrium at the final temperature, Tf.
 
  • #5
But how can you set it up?

I tried mcat=mcat but you get 75=100 which is obviously not true..? Can you pleas explain how to solve the q=mcat problem? I'm really sorry I just don't get it...
 
  • #6
I tried mcat=mcat but you get 75=100 which is obviously not true

You can't eliminate the ∆Ts, they aren't the same. Do you know what ∆T means? It is the difference between the final and initial temperatures of the liquid, so ∆T = Tf - Ti. Knowing this, you can complete your equations Q1 and Q2. What's the expression for ∆T for the water at 245 K? What's ∆T for the water at 365 K? You know the initial temperature for each, and you want to find Tf which will be the equilibrium temperature after the two mix together. And as I said above, energy is conserved, so Q1 + Q2 = 0. You need to solve this equation for Tf.

See if that helps. I can't say much more without just giving you the solution, so try to think through what I've said and see how far you can get.
 
  • #7
Okay, thank you!

I ended up getting 312.143 K which is a little off from 314. Did you guys get 314 or 312.1 like me?

75(Final-245) + 100(Final-365)=0 ("c" cancels)
75x -183675 + 100x - 36500 = 0 (let "x" = temp final)
175x-54625=0
x=312.143
 
  • #8
75x -183675 + 100x - 36500 = 0 (let "x" = temp final)
175x-54625=0
Check your math carefully. You have an extra number in the 183675 but I think it might be a typo, so I'm not sure where you went wrong. I get 314 K after rounding.
 
  • #9
Opps, yes! A typ-o!

And I did get 313.6 when I tried it again. Thank you so much for your continued help and patience! =) I really appreciate it because I know you didn't have to do it but you were willing to stick with me until I got it, which was really nice of you. Thanks again. :smile:
 
  • #10
You're welcome. :smile:
 

1. How does temperature affect the properties of a liquid?

The temperature of a liquid can affect its density, viscosity, and vapor pressure. As temperature increases, the molecules in the liquid gain kinetic energy and move more quickly, causing the liquid to expand and become less dense. This also decreases the viscosity, making it easier for the liquid to flow. Additionally, as temperature increases, the vapor pressure of the liquid increases as well, potentially leading to evaporation.

2. What happens to the molecules of a liquid when its temperature is increased?

When the temperature of a liquid is increased, the molecules gain kinetic energy and move more quickly. This causes the molecules to spread out and take up more space, resulting in the expansion of the liquid. The increased movement of the molecules also leads to a decrease in intermolecular forces, making the liquid less viscous and more likely to evaporate.

3. How does the final temperature of two samples of the same liquid but at different temperatures compare?

The final temperature of two samples of the same liquid but at different temperatures will depend on the amount of each sample and their initial temperatures. However, if the samples are mixed together, the final temperature will be somewhere between the initial temperatures, as the molecules of the hotter sample transfer some of their energy to the molecules of the colder sample until thermal equilibrium is reached.

4. What is the difference between heat and temperature in relation to a liquid?

Heat and temperature are related but different concepts. Temperature is a measure of the average kinetic energy of the molecules in a substance, while heat is the transfer of energy from a warmer object to a cooler object. In terms of a liquid, an increase in heat will cause an increase in temperature, resulting in the molecules moving more quickly and potentially changing the properties of the liquid.

5. How does the specific heat capacity of a liquid affect its temperature change?

The specific heat capacity of a liquid is the amount of energy required to raise the temperature of 1 gram of the liquid by 1 degree Celsius. A liquid with a higher specific heat capacity will require more energy to increase its temperature compared to a liquid with a lower specific heat capacity. This means that a liquid with a higher specific heat capacity will experience a smaller temperature change when the same amount of heat is added compared to a liquid with a lower specific heat capacity.

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