What is the heat change in J associated with 44 g of solid methanol at -149 oC changing to liquid at -83 oC?
c(methanol) (liq) = 2.47 J/(g.K)
c(methanol) (s) = 1.85 J/ (g.K)
ÄHfus(methanol) = 3.17 kJ/mol
The freezing point of methanol is -98 oC
Make a table
heat warming solid=mass*csolid*(-98+149)
heat melting solid to liquid=mass*Hf
heat used heating liquid=mass*cliwuid(-83+98)
add the heats.
To find the heat change associated with the given process, we can break it down into two steps: the heat change during the warming of the solid methanol from -149 oC to -98 oC, and the heat change during the phase change from solid to liquid at -98 oC.
Step 1: Calculating the heat change during warming
To calculate the heat change during warming, we need to use the specific heat capacity (c) of solid methanol. The specific heat capacity of solid methanol is given as 1.85 J/(g.K).
First, we need to calculate the temperature change during the warming process. The initial temperature is -149 oC, and the final temperature is -98 oC. The temperature change is:
ΔT = final temperature - initial temperature
ΔT = -98 oC - (-149 oC)
ΔT = -98 oC + 149 oC
ΔT = 51 oC
Next, we can calculate the heat change during the warming process using the formula:
q = m * c * ΔT
where:
q = heat change
m = mass of the substance
c = specific heat capacity
ΔT = temperature change
The mass of solid methanol is given as 44 g. Plugging in the values, we get:
q = 44 g * 1.85 J/(g.K) * 51 oC
q = 4124.4 J
So, the heat change during the warming of solid methanol is 4124.4 J.
Step 2: Calculating the heat change during the phase change
To calculate the heat change during the phase change from solid to liquid, we need to use the enthalpy of fusion (ΔHfus) of methanol and the molar mass of methanol.
The enthalpy of fusion of methanol is given as 3.17 kJ/mol.
The molar mass of methanol (CH3OH) is 32.04 g/mol.
We can calculate the moles of methanol using the mass and molar mass:
moles = mass / molar mass
moles = 44 g / 32.04 g/mol
moles = 1.373 mol
Now we can calculate the heat change during the phase change using the formula:
q = moles * ΔHfus
Plugging in the values, we get:
q = 1.373 mol * 3.17 kJ/mol * 1000 J/1 kJ
q = 4360.41 J
So, the heat change during the phase change from solid to liquid is 4360.41 J.
To find the total heat change, we simply add the heat changes from the two steps:
Total heat change = heat change during warming + heat change during phase change
Total heat change = 4124.4 J + 4360.41 J
Total heat change = 8484.81 J
Therefore, the heat change associated with 44 g of solid methanol changing to liquid methanol is 8484.81 J.