the specific heat capacity of gold is .13 J/g°C. Calculate the specific heat capacity of gold in cal/g°C. Calculate the specific heat capacity of gold in J/mol°C.
Calculate the amount of energy required in joules to heat 2.5 kg of water from 18.5°C to 55.0°C
I think for these you have to use the equation Q=(s)(m)(Δt). I know how to get the numbers for the letters, but i don't know how you do it when they only give you 2 numbers when you need at least 3 to solve.
To convert the specific heat capacity of gold from J/g°C to cal/g°C, you can use the conversion factor 1 cal = 4.184 J.
Specific Heat Capacity of Gold in cal/g°C:
Specific heat capacity of gold = 0.13 J/g°C
1 cal = 4.184 J
So, to convert J to cal, you divide the specific heat capacity of gold by 4.184:
0.13 J/g°C / 4.184 J/cal = 0.0311 cal/g°C
Therefore, the specific heat capacity of gold is approximately 0.0311 cal/g°C.
To calculate the specific heat capacity of gold in J/mol°C, you need to know the molar mass of gold. The molar mass of gold is 197 g/mol.
Specific Heat Capacity of Gold in J/mol°C:
To convert from g to mol, divide the specific heat capacity of gold in J/g°C by the molar mass of gold:
0.13 J/g°C / 197 g/mol = 0.000659 J/mol°C
Therefore, the specific heat capacity of gold is approximately 0.000659 J/mol°C.
Now, let's move on to the calculation of the amount of energy required to heat 2.5 kg of water from 18.5°C to 55.0°C using the equation Q = (s)(m)(Δt).
Q = (s)(m)(Δt)
Where:
Q is the amount of energy required (in joules)
s is the specific heat capacity of water (4.184 J/g°C or 4.184 J/g*K)
m is the mass of water (in grams)
Δt is the change in temperature (in °C or K)
Since you have the mass of water given in kilograms, you will need to convert it to grams.
m = 2.5 kg * 1000 g/kg = 2500 g
Now, you have all the values needed to solve the equation.
s = 4.184 J/g°C (specific heat capacity of water)
m = 2500 g (mass of water)
Δt = (55.0°C - 18.5°C) = 36.5°C
Q = (4.184 J/g°C)(2500 g)(36.5°C) = 387,010 J
Therefore, the amount of energy required to heat 2.5 kg of water from 18.5°C to 55.0°C is approximately 387,010 Joules.