The heat of neutralization of HCl(aq) and NaOH(aq) is -55.90 kJ/mol of water produced. If 50.00 mL of 1.16 M NaOH at 25.15 ºC is added to 25.00 mL of 1.79 M HCl at 26.34 ºC in a plastic-foam cup calorimeter, what willthe solution temperature be immediately after the neutralization reaction has occurred? You may assume that each solution has a density and specific heat that is the same as for pure water and that no heat escapes from the calorimeter.
I have already found the number of moles: 0.058 mol OH and 0.04475 mol H, and determined that HCl is the limiting reagent.
I have also found that (0.04475 mol H)(-55.9 kJ/mol) = -2.50 kJ.
I'm confused as to where to go from here. I don't need answers, but I would like to see formulas so I can solve it myself.
Well, since you have determined that HCl is the limiting reagent, it means that all of the HCl will be completely reacted with NaOH. Now, we need to use the heat transfer equation to find the change in temperature.
The heat transfer equation is given by:
q = mcΔT
Where q is the heat gained or lost by the system, m is the mass of the solution, c is the specific heat capacity of the solution, and ΔT is the change in temperature.
In this case, we want to find the change in temperature, so we can rearrange the equation:
ΔT = q / (mc)
Now, we know that q is -2.50 kJ (negative because it's lost by the system), and we can assume the density and specific heat capacity of the solution are the same as for pure water, which are 1 g/mL and 4.18 J/gºC, respectively.
To find the mass of the solution, we can add the masses of the HCl and NaOH solutions. Since mass = volume × density, we have:
mass(HCl) = 25.00 mL × 1.00 g/mL (assuming density is the same as pure water)
mass(NaOH) = 50.00 mL × 1.00 g/mL
mass(solution) = mass(HCl) + mass(NaOH)
Using the values you provided, calculate the mass of the solution. Then substitute the values into the equation above to find the change in temperature (ΔT). Finally, add the change in temperature to the initial temperature (25.15 ºC) to find the solution temperature immediately after the neutralization reaction.
Keep in mind that this is just a guideline to help you solve the problem yourself. Let me know if you have any more questions or need further assistance!
To determine the final temperature of the solution immediately after the neutralization reaction, you can use the concept of heat transfer in a calorimeter, which is given by the equation:
q = mcΔT
Where:
q is the heat transfer (in joules)
m is the mass of the solution (in grams)
c is the specific heat capacity of the solution (assumed to be the same as water, 4.18 J/g·°C)
ΔT is the change in temperature (in °C)
In this case, we know the heat transfer (q) from the reaction is -2500 J (since it's negative), the mass of the solution (which is the sum of the masses of NaOH and HCl), and we need to find ΔT.
1. Calculate the mass of NaOH:
mass of NaOH = volume of NaOH x density of water x molar mass of NaOH
mass of NaOH = 50.00 mL x 1 g/mL x 39.997 g/mol (molar mass of NaOH)
mass of NaOH = 199.85 g
2. Calculate the mass of HCl:
mass of HCl = volume of HCl x density of water x molar mass of HCl
mass of HCl = 25.00 mL x 1 g/mL x 36.461 g/mol (molar mass of HCl)
mass of HCl = 911.53 g
3. Calculate the total mass of the solution:
total mass of the solution = mass of NaOH + mass of HCl
total mass of the solution = 199.85 g + 911.53 g
total mass of the solution = 1111.38 g
4. Calculate the change in temperature:
q = mcΔT
-2500 J = (1111.38 g)(4.18 J/g·°C)(ΔT)
-2500 J = 4642.42 g·°C(ΔT)
ΔT = -2500 J / 4642.42 g·°C
ΔT = -0.538 °C
5. Calculate the final temperature of the solution:
final temperature = initial temperature + ΔT
final temperature = 26.34 °C - 0.538 °C
final temperature = 25.80 °C
So, the solution temperature will be approximately 25.80 °C immediately after the neutralization reaction has occurred.
To determine the solution temperature immediately after the neutralization reaction, you need to use the concept of heat transfer. The heat released in the neutralization reaction is equal to the heat absorbed by the solution and the calorimeter. This heat transfer can be calculated using the following equation:
q = mcΔT
Where:
q = heat transfer (in joules or calories)
m = mass of the solution (in grams)
c = specific heat capacity of the solution (in J/g·°C or cal/g·°C)
ΔT = change in temperature (in °C)
Since the heat released (-2.50 kJ) is given in kJ and the specific heat capacity of the solution is assumed to be the same as pure water, which is 4.18 J/g·°C, we will need to convert the units.
Step 1: Convert the heat released to joules:
-2.50 kJ x 1000 J/kJ = -2500 J
Step 2: Determine the mass of the solution:
To find the mass of the solution, you can assume the density of the solution is the same as water and calculate the mass using the formula:
Density = mass/volume
Given that the density of water is 1 g/mL, and the volumes of NaOH and HCl used are 50.00 mL and 25.00 mL, respectively:
mass of NaOH solution = (50.00 mL)(1 g/mL) = 50.00 g
mass of HCl solution = (25.00 mL)(1 g/mL) = 25.00 g
The total mass of the solution is the sum of the masses of NaOH and HCl solutions:
mass of solution (m) = mass of NaOH solution + mass of HCl solution
Step 3: Calculate the change in temperature (ΔT):
Since the calorimeter is assumed to be insulated and no heat escapes, the heat released by the reaction will be absorbed by the solution and the calorimeter, causing their temperature to increase. We can assume the final temperature of the solution and calorimeter is the same.
To calculate the change in temperature, you can use the equation:
ΔT = q / (m x c)
Step 4: Solve for the final temperature:
The final temperature can be found by subtracting the change in temperature from the initial temperature of the solution. In this case, the initial temperature of the NaOH solution is 25.15 ºC, and the initial temperature of the HCl solution is 26.34 ºC.