If you have an insulated glass of water at 25 oC containing 10 fluid oz at 25 oC, how much ice would you have to add to end up with a final temperature of 0 oC and no ice left?

Convert 10 oz to grams. There are 28.35 g to an oz.

(mass ice x heat fusion ice) + [(mass water x specific heat water x (Tfinal-Tinitial)] = 0
Solve for Tfinal, the only unknown. Post your work, IN DETAIL, if you get stuck.

283.5 x .5 + 10 x 1 X (X)=0

To calculate how much ice you need to add to the insulated glass of water to reach a final temperature of 0 degrees Celsius with no ice remaining, you can use the principle of heat transfer and the specific heat capacities of water and ice.

Here are the steps to calculate the amount of ice needed:

Step 1: Determine the initial heat content (Q1) of the water using the formula:
Q1 = mass × specific heat capacity × change in temperature

Given:
Mass of water (m1) = 10 fluid oz = 295.735 mL (since 1 fluid oz is approximately equal to 29.574 mL)
Specific heat capacity of water (c1) = 4.18 J/g°C (joule per gram per degree Celsius)
Temperature change (ΔT1) = 25 °C - 0 °C (initial temperature - final temperature)

Convert mass of water from mL to grams:
Mass of water (m1) = 295.735 g (since 1 mL of water has a mass of approximately 1 g)

Now calculate the initial heat content of the water:
Q1 = 295.735 g × 4.18 J/g°C × (25 °C - 0 °C)
Q1 = 30941.3075 J

Step 2: Determine the heat content (Q2) of melting the ice. When ice melts, it absorbs heat without changing temperature. The heat content of melting ice is given by the formula:
Q2 = mass × heat of fusion

Given:
Heat of fusion of ice (Hf) = 334 J/g (joules per gram)

Q2 represents the heat required to melt all the ice and bring it to water at 0 °C.

Now, let's say you have 'X' grams of ice. The mass of this ice will be equal to the mass of water that has to be melted in order to reach the final temperature. Therefore, we can write the equation as:
Q2 = X g × 334 J/g

Step 3: The final heat content (Qf) of the water at 0 °C is obtained by adding the heat content of the melted ice (Q2) to the initial heat content (Q1).
Qf = Q1 + Q2

Since the final temperature is 0 °C, the final heat content (Qf) of the water will be zero, as the water is at its freezing point.

Therefore, Qf = 0

Now, we can substitute the values of Q1 and Q2 into the equation:
0 = Q1 + X g × 334 J/g

Now, solve for 'X' to determine the mass of ice needed.

X g × 334 J/g = -30941.3075 J (negative sign indicates heat lost by water is equal to heat gained by ice)

Solving for 'X':
X g = -30941.3075 J / 334 J/g
X g ≈ -92.525

Since mass cannot be negative, we discard the negative sign. Therefore, the mass of ice needed to reach a final temperature of 0 °C is approximately 92.525 g.

Please note that this calculation assumes that there is no heat transfer to the surroundings and that the entire amount of ice added will melt completely to reach the final temperature of 0 °C.