Glauber's salt undergoes a phase transition according to the following equation:
Na2SO4*10H2O(s)--> Na2SO4*10H2O(l) ∆H = 74.4 kJ/mol
Calculate the mass (g) of Glauber's salt (use the masses to two decimal places found in the front of your text) needed to lower the temperature of air in a room by 7.8oC. The mass of air in the room is 578 kg; the specific heat of air is 1.2J/g-C.
I'm not sure what formula to use here, can i get a hint please?
q = mass air(in g) x specific heat air x delta T
Solve for q (which is delta H)
Convert to g of the salt to give that delta H.
Q=578000(1.2)(7.8)= 5410080.
Im not sure I understand the last part with the grams of the salt.
You're right so far. 5.41E6 J = 5.41E3 kJ.
molar mass Glauber's salt is 322 so here is what you have.
322 g salt absorbs 74.4 kJ. So how many g will it take to absorb 5.41E3 kJ. That will be
322 x (5.41E3 kJ/74.4 kJ) = ? g of the salt.
Thank you so much for all your help.
To solve this problem, we will use the equation q = m * c * ∆T, where:
- q is the heat transferred (in Joules),
- m is the mass of the substance being heated or cooled (in grams),
- c is the specific heat capacity of the substance (in J/g-°C), and
- ∆T is the change in temperature (in °C).
In this case, we want to calculate the mass of Glauber's salt needed to lower the temperature of the air in a room. To do this, we'll calculate the amount of heat needed to lower the temperature (∆T) and then use the equation above to find the mass (m) of Glauber's salt.
Now let's break down the steps to solve the problem:
1. Calculate the heat transferred (q):
We want to lower the temperature of air in the room by 7.8°C. The mass of air in the room is given as 578 kg, which is equal to 578,000 grams. The specific heat capacity of air is given as 1.2 J/g-°C. Using the equation q = m * c * ∆T, we can calculate q as follows:
q = (mass of air) * (specific heat capacity of air) * (∆T)
q = 578,000 g * 1.2 J/g-°C * (-7.8°C)
2. Convert the heat transferred (q) to kilojoules:
The heat transfer unit in the given phase transition equation is kJ/mol, so we need to convert the heat transferred (q) from Joules to kilojoules. Divide the result obtained in step 1 by 1000:
q (in kJ) = q (in J) / 1000
3. Use the equation ∆H = q/m to calculate the mass (m) of Glauber's salt:
Rearrange the equation to solve for mass (m):
m = q / ∆H
4. Substitute the values into the equation and calculate the mass (m) of Glauber's salt.
Let me know if you need further assistance with the calculations!