Temperature when a 40 g ice cube at 0.0C is dropped into 500ml of water at 30C?

[Maggie 13]

I am new to this ... I mean forums never done it before so bear with me.
Need help with this chem question
A 40 g ice cube at 0.0C is dropped into %00ml of water at 30C. Assuming the ice melts completely,find the final temperature.
I need the equation to use and the math explained step by step if some one can help
Thanks

these are the formulas that i know i need to use
mc(delta) t... (don't know how to get the symbol for delta)
nH

 

[chemisttree]

I assume that '%00ml' refers to 500 mL?

Try editing your post to clearly refer to the formulas you know or intend to use.

Hint: At 0C, ice begins to melt. This heat is the heat of fusion. After melting, the material (now 40 g of water) is still at 0C and has a heat capacity that is different from that of ice.

 

[Blueshift5]

2O (delta) Hf

Hello there! Don't worry, we are here to help. To answer your question, we will need to use the heat transfer equation:

Q = m x c x ΔT

Where:
Q = heat transfer (in Joules)
m = mass (in grams)
c = specific heat capacity (in J/g°C)
ΔT = change in temperature (in °C)

First, let's convert the mass of the ice cube into kilograms:
40 g = 0.04 kg

Next, let's calculate the initial heat of the ice cube:
Q1 = m x c x ΔT
Q1 = (0.04 kg) x (2.09 J/g°C) x (0.0°C - (-10°C))
Q1 = 8.36 J

Now, let's calculate the heat needed to melt the ice:
Q2 = nH2O x ΔHf
Q2 = (0.04 kg) x (334 J/g)
Q2 = 13.36 J

Since the ice is melting, the heat transfer from the ice to the water is equal to the heat needed to melt the ice:
Q1 = Q2
8.36 J = 13.36 J
Therefore, the total heat transfer is 21.72 J.

Now, we can use the heat transfer equation to find the final temperature of the water:
Q = m x c x ΔT
21.72 J = (0.5 kg) x (4.18 J/g°C) x (Tf - 30°C)
Tf - 30°C = 5.2°C
Tf = 35.2°C

Therefore, the final temperature of the water will be 35.2°C.

I hope this helps! Just remember to always use the correct units and follow the steps of the equation. Good luck with your studies!