Glauber's salt undergoes a phase transition according to the following equation:
Na2SO4*10H2O(s)--> Na2SO4*10H2O(l) DH = 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 6.8oC. The mass of air in the room is 549.2 kg; the specific heat of air is 1.2J/g-C.
How much heat must be extracted from the room?
mass air x specific heat air x DT.
549200 g x 1.2 x 6.8 = ??
322.106 g of the salt will extract 74.7. You want to know how much it will take to extract ??.
Check my work.
how did you get 322.106 g?
To calculate the mass of Glauber's salt needed to lower the temperature of air in a room, we need to use the formula:
q = m_air * c_air * ΔT_air = -m_salt * ΔH
Where:
- q is the heat absorbed by the salt and released by the air (assumed to be negative since heat is transferred from the salt to the air).
- m_air is the mass of air in the room.
- c_air is the specific heat of air.
- ΔT_air is the change in temperature of air in Celsius.
- m_salt is the mass of Glauber's salt.
- ΔH is the enthalpy change for the phase transition.
Rearranging the formula, we can solve for the mass of Glauber's salt:
m_salt = - (m_air * c_air * ΔT_air) / ΔH
Now let's substitute the given values into the formula:
m_air = 549.2 kg = 549200 g
c_air = 1.2 J/g-°C
ΔT_air = 6.8 °C
ΔH = 74.4 kJ/mol = 74.4 kJ/ (Na2SO4*10H2O)
To proceed further, we need to know the molar mass of Na2SO4*10H2O, which can be found in the front of your text. Please provide the molar mass so we can calculate the mass of Glauber's salt needed.