Chemistry
The molar heat capacity of butane under constant pressure Cp=19.4 + 0.233 T J.mol' '.K' . Calculate the quantity of heat needed to increase the temperature from 27"C to 127 ° Cu under1 atm pressure.
To calculate the quantity of heat needed, we can use the formula:
Q = n * Cp * ΔT
where:
Q = quantity of heat
n = number of moles
Cp = molar heat capacity (J/mol·K)
ΔT = change in temperature (K)
First, we need to calculate the change in temperature:
ΔT = final temperature - initial temperature
= 127 °C - 27 °C
= 100 °C
Next, we need to convert the change in temperature from Celsius to Kelvin:
ΔT = 100 °C + 273.15
= 373.15 K
Now, we need to calculate the number of moles.
To calculate the number of moles, we need the molar mass of butane (C₄H₁₀).
The molar mass of carbon (C) = 12.01 g/mol
The molar mass of hydrogen (H) = 1.01 g/mol
The molar mass of butane (C₄H₁₀):
= (4 × C) + (10 × H)
= (4 × 12.01 g/mol) + (10 × 1.01 g/mol)
= 48.04 g/mol + 10.10 g/mol
= 58.14 g/mol
Now, we need to convert the quantity of butane from grams to moles.
To calculate the number of moles, we can use the formula:
n = mass / molar mass
Given that the pressure is 1 atm, the volume is not mentioned. Therefore, we can assume that the system is at constant volume, which means the number of moles remains constant.
Now, substituting the values into the formula:
n = mass / molar mass
= 1g / 58.14 g/mol
= 0.0172 mol (rounded to 4 decimal places)
Finally, we can calculate the quantity of heat using the formula:
Q = n * Cp * ΔT
= 0.0172 mol * (19.4 + 0.233 T) J/mol·K * 373.15 K
Note: Since the temperature (T) in the formula is not explicit, we can assume it to be the average temperature between the initial and final temperatures, i.e., (27°C + 127°C) / 2 = 77°C
Q = 0.0172 mol * (19.4 + 0.233 * 77) J/mol·K * 373.15 K
To calculate the quantity of heat needed to increase the temperature of butane, we need to use the formula:
q = n * Cp * ΔT
where:
q is the quantity of heat (in joules)
n is the number of moles of butane
Cp is the molar heat capacity (in joules per mole per Kelvin)
ΔT is the change in temperature (in Kelvin)
First, let's convert the temperature from Celsius to Kelvin:
27°C + 273.15 = 300.15 K (Initial temperature)
127°C + 273.15 = 400.15 K (Final temperature)
Now we need to calculate the change in temperature:
ΔT = Final temperature - Initial temperature
ΔT = 400.15 K - 300.15 K = 100 K
Next, let's calculate the quantity of heat:
q = n * Cp * ΔT
Since we don't have the number of moles (n) provided in the question, we can't directly calculate the quantity of heat. However, we can assume that we have 1 mole of butane, since it is commonly used as the basis in thermodynamics calculations.
Substituting the given values:
q = (1 mole) * (19.4 + 0.233 T J.mol^-1 K^-1) * (100 K)
Now, let's calculate the quantity of heat:
q = 19.4 + 0.233 * 100 J = 19.4 + 23.3 J = 42.7 J
Therefore, the quantity of heat needed to increase the temperature of 1 mole of butane from 27°C to 127°C under 1 atm pressure is approximately 42.7 joules.