Urea (NH2CONH2), an important nitrogen fertilizer, is produced industrially by the reaction 2NH3(g)+ CO2(g)--> NH2CONH2(aq)+ H2O(l). Given that delta G = -13.6 kj/mol, calculate delta G at 25 degree C.for the following condition.
40 atm NH3 , 40 atm CO2 , 2.0 M NH2CONH2
I am confused about how to set the problem up. Please help.
Well, setting up this problem can be as confusing as trying to balance on a unicycle while juggling watermelons. But fear not, for Clown Bot is here to help you navigate through this nitrogen-filled maze.
To calculate the delta G at 25 degrees Celsius, we need to use the formula:
ΔG = ΔG° + RTln(Q)
where ΔG° is the standard free energy change, R is the ideal gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin, Q is the reaction quotient, and ln stands for the natural logarithm.
Now, let's break it down step by step, just like a clown would break down a balloon animal:
Step 1: Convert the given pressure of NH3 and CO2 to partial pressures.
Since the reaction is taking place in the gas phase, we need to calculate the partial pressure of NH3 and CO2. As we have a total pressure of 40 atm for each, the partial pressures will also be 40 atm.
Step 2: Calculate the reaction quotient (Q).
The reaction quotient Q is calculated by taking the product of the concentrations (in this case, partial pressures) of the reactants and dividing it by the product of the concentrations of the products, each raised to the power of their respective stoichiometric coefficients.
Q = (P(NH2CONH2) * P(H2O)) / (P(NH3)^2 * P(CO2))
Given that the concentration of NH2CONH2 is 2.0 M, and the partial pressures of NH3 and CO2 are both 40 atm, we can substitute these values into the equation.
Q = (2.0 * 1) / (40^2 * 40)
In other words, Q = 1 / 64000
Step 3: Convert the temperature from degrees Celsius to Kelvin.
To convert Celsius to Kelvin, just add 273 to the temperature.
T = 25 + 273 = 298 K
Step 4: Substitute the values into the equation.
ΔG = ΔG° + RTln(Q)
Given that ΔG° = -13.6 kJ/mol and R = 8.314 J/(mol·K), we need to convert ΔG° to J.
ΔG° = -13.6 kJ/mol * (1000 J/ 1 kJ) = -13,600 J/mol
Now, we can plug in all the values into the equation and calculate the delta G:
ΔG = -13,600 J/mol + (8.314 J/(mol·K)) * (298 K) * ln(1/64000)
And voila! Solve that mathematical circus and you'll get your answer.
To calculate the change in Gibbs free energy (ΔG) at 25 °C for the given conditions, we can use the equation:
ΔG = ΔG° + RT ln(Q)
where:
ΔG is the change in Gibbs free energy under the given conditions
ΔG° is the standard Gibbs free energy change (given as -13.6 kJ/mol)
R is the gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin (25 °C = 298 K)
ln is the natural logarithm
Q is the reaction quotient
First, let's calculate the reaction quotient (Q):
Q = [NH2CONH2] / ([NH3]^2 * [CO2])
Given:
[NH3] = 40 atm (partial pressure)
[CO2] = 40 atm (partial pressure)
[NH2CONH2] = 2.0 M (concentration)
Convert the concentration of NH2CONH2 to partial pressure:
Use the Ideal Gas Law, PV = nRT:
PV = nRT
Partial pressure (P) = concentration (C) * R * T
Partial pressure of NH2CONH2:
[NH2CONH2] = 2.0 M * 0.0821 L·atm/(mol·K) * 298 K
[NH2CONH2] = 48.674 atm
Now we can substitute the values into the equation:
ΔG = -13.6 kJ/mol + (8.314 J/(mol·K) * 298 K * ln(48.674 atm/ (40 atm)^2 * (40 atm)))
Make sure to convert the units to match, in this case, we are using J and atm.
ΔG = -13600 J/mol + (8.314 J/(mol·K) * 298 K * ln(48.674 atm/ (40 atm)^2 * (40 atm)))
Simplifying the equation should give you the final value for ΔG.
To calculate the delta G at 25 degrees Celsius for the given conditions, we can use the Gibbs free energy equation:
ΔG = ΔG° + RT ln(Q)
Where:
ΔG is the change in Gibbs free energy
ΔG° is the standard Gibbs free energy change at standard conditions (1 atm and 25°C)
R is the gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin
Q is the reaction quotient, which is calculated using the concentrations of the reactants and products
In this case, we are given the values for the concentrations and the reaction conditions. We can set up the reaction quotient (Q) using the concentrations:
Q = [NH2CONH2] / ([NH3]^2[CO2])
Substituting the values:
Q = (2.0 M) / ((40 atm)^2 * (40 atm))
Now we can calculate the delta G at 25 degrees Celsius by substituting the values into the equation:
ΔG = ΔG° + RT ln(Q)
Since the question asks for ΔG at 25 degrees Celsius, we need to convert the temperature to Kelvin:
Temperature in Kelvin (T) = (25°C + 273.15) K = 298.15 K
Now we can calculate ΔG using the given value of ΔG° = -13.6 kJ/mol:
ΔG = -13.6 kJ/mol + (8.314 J/(mol·K) * 298.15 K * ln(Q))
Note: We need to convert the value of ΔG° from kJ/mol to J/mol before using it in the equation.
Finally, we can substitute the calculated value of Q into the equation and solve for ΔG to obtain the final result.