From the data below, calculate the total heat (in J) needed to convert 22.00 g of icea t -6.00 C to liquid water at 0.500 C.

melting point at 1 atm: 0.0 C
Hfusion: 6.02 KJ/mol
cliquid: 4.21 J/g C
csolid: 2.09 J / g C

My answer is about 300 J short of the correct answer. It says it's 7670 J as the correct answer, but I keep getting 7,362 J. Not sure what I'm doing wrong.

My equations are as followed:
q= (1.22g)(2.09J/g C)(6.00C) = 15.29 (csolid, using Q=MC/\T equation)
q= (1.22g)(6.02KJ/mol)=7.3444 KJ (multiply this by 1,000 to make it into Joules = 7344)
(q=mHFusion equation)
q= (1.22g)(4.21J/g C)(.5)= 2.56 J
(q=MC/\T equation, cliquid)
Add all these up and I get 7,362 J.

Well, it seems like you're close, but you may have overlooked a crucial step in your calculations. Let's break it down together and see if we can identify the missing piece:

First, we need to calculate the heat required to raise the temperature of the ice from -6.00°C to 0.0°C. According to your equation, you correctly used the specific heat capacity of the solid (csolid). However, there seems to be a small error in the calculation. Let's fix it:

q = (22.00 g)(2.09 J/g°C)(6.00°C) = 277.44 J

Now, let's move on to the next step. We need to account for the heat required to melt the ice into liquid water. You correctly used the heat of fusion (Hfusion) equation, but you used the mass of the ice as 1.22 g instead of 22.00 g. Let's correct that:

q = (22.00 g)(6.02 kJ/mol) = 132.44 kJ

To convert this into joules, we need to multiply it by 1000:

q = 132,440 J

Finally, we need to find the heat required to raise the temperature of the liquid water from 0.0°C to 0.5°C. You correctly used the specific heat capacity of the liquid (cliquid) in your equation. However, you used a mass of 1.22 g instead of 22.00 g. Let's fix that as well:

q = (22.00 g)(4.21 J/g°C)(0.5°C) = 46.41 J

Now, let's add up all the heat values:

277.44 J + 132,440 J + 46.41 J = 132,763.85 J

So the correct answer should be approximately 132,764 J, which is a bit more than the 7,670 J you mentioned earlier. It seems like you mistakenly forgot to convert the heat of fusion from kJ to J, which caused the discrepancy in your results. Keep up the good work, and remember to always double-check your units and conversions!

To calculate the total heat needed, we need to consider three steps:

Step 1: Heating the ice from -6.00°C to 0.00°C (cliquid)
q1 = (mass)(specific heat)(change in temperature)
q1 = (22.00g)(2.09 J/g°C)(0.00°C - (-6.00°C))
q1 = (22.00g)(2.09 J/g°C)(6.00°C)
q1 = 277.02 J

Step 2: Melting the ice at 0.00°C to liquid water at 0.00°C (fusing)
q2 = (mass)(heat of fusion)
q2 = (22.00g)(6.02 kJ/mol)(1 mol/18.02 g)(1000 J/1 kJ)
q2 = 815.98 J

Step 3: Heating the liquid water from 0.00°C to 0.500°C (cliquid)
q3 = (mass)(specific heat)(change in temperature)
q3 = (22.00g)(4.21 J/g°C)(0.50°C - 0.00°C)
q3 = (22.00g)(4.21 J/g°C)(0.50°C)
q3 = 46.43 J

Now add up the three steps to get the total heat needed:
Total heat = q1 + q2 + q3
Total heat = 277.02 J + 815.98 J + 46.43 J
Total heat = 1139.43 J

Based on the calculations, the correct answer should be 1139.43 J, which is different from both the answer you obtained (7362 J) and the provided correct answer (7670 J). It seems there might be a mistake in the given data or in the calculations shown.

To calculate the total heat needed to convert the ice at -6.00 °C to liquid water at 0.500 °C, we need to consider the energy required for three steps: heating the ice from -6.00 °C to 0.00 °C, melting the ice at 0.00 °C, and heating the liquid water from 0.00 °C to 0.500 °C.

Let's go through the calculations step by step:

1. Heating the ice from -6.00 °C to 0.00 °C:
q1 = (mass of ice) x (specific heat capacity of solid) x (change in temperature)
= (22.00 g) x (2.09 J/g°C) x (0.00 °C - (-6.00 °C))
= 22.00 g x 2.09 J/g°C x 6.00 °C
= 277.32 J

2. Melting the ice at 0.00 °C:
q2 = (mass of ice) x (heat of fusion)
= (22.00 g) x (6.02 kJ/mol)
Since the molar mass of water is 18.02 g/mol, we need to convert kJ to J by multiplying by 1000:
= (22.00 g) x (6.02 kJ/mol) x (1000 J/1 kJ)
≈ 7962.8 J

3. Heating the liquid water from 0.00 °C to 0.500 °C:
q3 = (mass of liquid water) x (specific heat capacity of liquid) x (change in temperature)
= (22.00 g) x (4.21 J/g°C) x (0.500 °C - 0.00 °C)
= 23.21 J

Now, let's add these three quantities to get the total heat:

Total heat = q1 + q2 + q3
= 277.32 J + 7962.8 J + 23.21 J
≈ 8263.33 J

From your calculations, it seems you made a mistake in calculating the heat of fusion (q2) and used the specific heat capacity of the solid (csolid) instead of the heat of fusion, which led to a significant difference in the final answer.

realized my mistake