If 50.0 mL of ethanol (density = 0.789 gmL) initially at 7.0 °C
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Question

If 50.0 mL of ethanol (density = 0.789 g>mL) initially at 7.0 °C
is mixed with 50.0 mL of water (density = 1.0 g/mL) initially at
28.4 °C in an insulated beaker, and assuming that no heat is
lost, what is the final temperature of the mixture?

Accepted Answer

Hey everyone, we're asked to calculate the final temperature of a mixture containing Beautiful and water, assuming that no heat is lost to the surroundings. To answer this question, we need to think about our relationship between water and Beautiful. So since water is losing heat, we're going to have the negative Q of our water and that's going to be equivalent to our positive Q. Of our beautiful since Beautiful is absorbing heat. Plugging in the formula that we've learned. We have negative times the mass of our water, times the specific heat of water times delta teeth is going to be equivalent to the mass of our beautiful times of specifically to beautiful times delta T. So let's go ahead and plug in these values. Starting off with our massive water. We can go ahead and find this by using dimensional analysis. We were told that we have 75 ml of each compound. So 75 ml Times the density of water which is 1.0 grams per one mill leader. And we're going to multiply this by its specific heat of 4.184 jewels over g times degrees C. And our change in T, which is going to be our final temperature minus 30.1°C. This is going to be equivalent to the massive beautiful which is again 75 mL. And we're going to use beautiful density which is 0.81 g over one mil leader. And we're going to multiply this by its specific heat of 2. jules over grams times degrees Celsius. And finally we have Our final temperature and we're going to subtract 5°C. So calculating this out and simplifying this a bit further, we're going to end up with -313.5 jewels over degrees C Times our final temperature -30.1°C. And that's going to be equivalent to 150.05 jules over degrees Celsius times our final temperature -5°C. And simplifying this a bit further, we end up with - .55 jewels over degrees C times our final temperature. And this is going to be equivalent to negative 10,186.6 jewels. And when we divide this all by 463.55 jewels over°C. And don't forget the negative, We end up with a final temperature Of 22.0°C. And this is going to be our final answer. So I hope this made sense. And let us know if you have any questions

If 50.0 mL of ethanol (density = 0.789 g>mL) initially at 7.0 °C is mixed with 50.0 mL of water (density = 1.0 g/mL) initially at 28.4 °C in an insulated beaker, and assuming that no heat is lost, what is the final temperature of the mixture?

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