Question

A student pours 46.8g of water at 17oC into a beaker containing 111.4g or water at 17oC. The density of water at 17oC is 1.00 g/mL.

(a) What is the final mass?

(b) What is the final temperature?

(c) What is the final density?

Answer 1

Add the volumes

Answer 2

160g

Answer 3

158.2 g

Answer 4

We can remember that density \(\rho = m/V\)
Solve this equation for the mass \(m\), then plug in the values for \(\varrho\), and \(V\)

Answer 5

So 160 * 1.00?

Answer 6

yes

Answer 7

so 160 g

Answer 8

yes 158.2 g

Answer 9

NB ( 1 cm^3 = 1 ml )

Answer 10

what does the NB stand for?

Answer 11

note well: \( 1\,[\text{cm}^3] = 1\,[\text{mL}]\))

Answer 12

Oh. Thanks.

Answer 13

OK, so you have (a),

what do you think about (b)?

Answer 14

would temperatures need to be added?

Answer 15

is temperature an extensive quantity, or intensive ?

Answer 16

intensive

Answer 17

right, so the temperature should become the average

Answer 18

(not the sum)

Answer 19

what is the average of 17°C and 17°C ?

Answer 20

17

Answer 21

* is suppose it really should be the weighted average,
but yes the temperatures are the same so the temperature wont change

Answer 22

makes sense?

Answer 23

not exactly

Answer 24

which bits are unclear?

Answer 25

how I am suppose to use the average to figure out the final temperature

Answer 26

i don't think you are expected calculate the temperature,

the temperatures are the same

Answer 27

so it would be 17 as the final?

Answer 28

yeah, if you mix so water that is 17°C, with some more water that is 17°C,
the temperature of the mixture will be 17°

Answer 29

Alright. That makes sense now.

Answer 30

Thanks.

Answer 31

If they were different temperatures, then the final temperature would be some in-between

Answer 32

Gotcha. It makes sense now.

Answer 33

so what do you got for (c) ?

Answer 34

You would multiple the final mass by the density to get volume.

Answer 35

which gives 160

Answer 36

So 160/160 = 1.00g/mL

Answer 37

(c) is asking for the final density,

we know that density (like temperature, but unlike mass) is an intensive quality,
i.e. density is a property of the material, rather than the object

Answer 38

the question states
The density of water at 17°C is 1.00 [g/mL].

We found the final temperature of the mixture to be 17°C.

Answer 39

you don't have you multiply or divide to get (c),

Answer 40

why would we need to know the temperature for the final density?

Answer 41

because the density of water is temperature dependent

Answer 42

Okay. Because of the intensive and extensive

Answer 43

So you only have to look at it? Not do any math?

Answer 44

right , there is no math for (c),
it is just: notice that our final temperature 17°C, is one at which we know the density to be 1 [g/mL]

Answer 45

what makes you realize that?

Answer 46

it's given in the question

Answer 47

we found the final temperature in (b),
and the question tell us the density of water at this temperature

Answer 48

Yeah.

Answer 49

if the temperatures were different, and we calculated a weighted average temperature, we might use a table to look up the density of water at the temperature

Answer 50

We are combining objects with the same intensive properties,

whereas, the extensive property (the mass) is the sum

the intensive properties (temperature and density) of the mixture will be equal.

Answer 51

because intensive is independent?

Answer 52

Yes, intensive properties are independent of the amount we have

Answer 53

That makes sense now.

Answer 54

Thank you again for the help.