the specific heat of water is 4.184 j/g °c. How many grams of water at 85 C would have to be added to raise 1.00 kg of water from 25.0 C to 50.0 C?

Please help I am not sure of where to start!

The sum of the heats gained has to be zero.

heataddedwater+heatstartingwater=0
massadded*c(50-85)+1kg*cw*(50-25)=0
solve for massadded.

why did you take 50-85??

(Tfinal-tempInitial)

So I got 714 grams of water but it doesnt seem right to me some how.

sounds ok to me, you are heating 1000 grams by 25 degrees, cooling 714 by 35 degrees... about equal

But looking at the question if you add 714 grams of water at temp 85C would 1000 g of water will raise from 25C to 50C. I feel like if you add that much water of 85C the water temp will be a lot more higher than 50 C

do the math:

heat lost=714*c*35=
heat gained=1000c*25=

are they equal?

Yes.

I think I get it now.
Thank you for your help!

To solve this problem, you can use the equation:

Q = mcΔT

Where:
Q is the amount of heat transferred
m is the mass of water
c is the specific heat of water
ΔT is the change in temperature

In this case, we want to find the mass of water (m), so we rearrange the equation:

m = Q / (cΔT)

First, let's calculate the heat transferred (Q) for the 1.00 kg of water that we want to raise from 25.0 °C to 50.0 °C. We can use the equation:

Q = mcΔT

Where:
m = 1.00 kg (mass of water)
c = 4.184 J/g °C (specific heat of water)
ΔT = 50.0 °C - 25.0 °C = 25.0 °C (change in temperature)

Now, we can substitute the values into the equation:

Q = (1.00 kg) x (1000 g/kg) x (4.184 J/g °C) x (25.0 °C)

Simplifying the equation:

Q = 1.00 kg x 1000 g/kg x 4.184 J/g °C x 25.0 °C

Q = 104,600 J

Now, we can substitute the calculated value of Q and the given values of c and ΔT into the equation to find the mass of water:

m = Q / (cΔT)

m = 104,600 J / (4.184 J/g °C x 85 °C)

Simplifying the equation:

m = 104,600 J / 354.14 J/g

m ≈ 295.6 g

Therefore, approximately 295.6 grams of water at 85 °C would need to be added to raise 1.00 kg of water from 25.0 °C to 50.0 °C.