To calculate the Gibbs free energy (G) at 700 K, we can use the formula: ( G = H - TS ). Given that ( H = -92 , \text{kJ/mol} ) and ( S = -0.199 , \text{kJ/(mol·K)} ), we first calculate ( TS = 700 , \text{K} \times -0.199 , \text{kJ/(mol·K)} = -139.3 , \text{kJ/mol} ). Then, substituting into the Gibbs equation:
[ G = -92 , \text{kJ/mol} - (-139.3 , \text{kJ/mol}) = 47.3 , \text{kJ/mol}. ]
Thus, the value for G at 700 K is 47.3 kJ/mol.
The volume can be calculated using the ideal gas law equation, V = (nRT) / P, where n is the number of moles (1.20 mol), R is the gas constant (8.31 LkPa/molK), T is the temperature in Kelvin (25 + 273 = 298 K), and P is the pressure (61.3 kPa). Substituting these values into the equation gives V = (1.20 mol * 8.31 LkPa/molK * 298 K) / 61.3 kPa ≈ 49.1 L.
To find the empirical formula, we need to determine the ratio of each element in the compound. First, find the moles of each element: K = 0.104 mol C = 0.052 mol O = 0.156 mol Next, divide each mole value by the smallest mole value to get the ratio: K = 0.104 mol / 0.052 mol = 2 C = 0.052 mol / 0.052 mol = 1 O = 0.156 mol / 0.052 mol = 3 Therefore, the empirical formula is K2CO3.
To determine the temperature at which the reaction becomes spontaneous, we can use the Gibbs free energy equation: ΔG = ΔH - TΔS. For a reaction to be spontaneous, ΔG must be less than 0. Given ΔH = -92 kJ/mol and ΔS = -199 kJ/(mol·K), we can set up the equation -92 kJ/mol - T(-199 kJ/(mol·K)) < 0. Solving for T gives T > 0.462 K, indicating that the reaction will be spontaneous at temperatures above this value.
The accepted value for the heat of solution of NH4Cl (ammonium chloride) is approximately +14.8 kJ/mol. This value represents the energy released or absorbed when one mole of NH4Cl dissolves in water at standard conditions.
The heat added can be calculated using the formula: q = nCpΔT, where q is the heat added, n is the number of moles, Cp is the molar heat capacity at constant pressure, and ΔT is the temperature change. Given n=5 moles, Cp for hydrogen gas is approximately 28.8 J/molK, and ΔT = 60°C - 30°C = 30 K, the heat added would be q = 5 mol * 28.8 J/molK * 30 K = 4320 J.
To find the value of G at 100 K, you can use the equation ΔG = ΔH - TΔS. Plugging in the values, you get ΔG = 27 kJ/mol - (100 K)(0.09 kJ/molK) = 18 kJ/mol. Therefore, the value for G at 100 K would be 18 kJ/mol.
The equation relating G, H, and S is G = H - TS, where T is the temperature in Kelvin. Plugging in the values given, G = 27 kJ/mol - 100 K * 0.09 kJ/(molK) = 27 kJ/mol - 9 kJ/mol = 18 kJ/mol. So, the value for G at 100 K is 18 kJ/mol.
G=18 kJ/mol
-18 kj/mol
It is spontaneous at 2000 K.
To find the Gibbs free energy change (ΔG) at 500 K, we can use the equation ΔG = ΔH - TΔS. Given that ΔH = -27 kJ/mol and ΔS = 0.09 kJ/(mol·K), we first convert the temperature to Kelvin (which is already given as 500 K). Then, substituting the values: ΔG = -27 kJ/mol - (500 K × 0.09 kJ/(mol·K)) = -27 kJ/mol - 45 kJ/mol = -72 kJ/mol. Thus, the value of G at 500 K is -72 kJ/mol.
DeltaG = DeltaH - TDeltaS dG = -54.32 kJ/mol - (54'32+273)K(-354.2J/molK) NB Thevtemperature is quoted in Kelvin(K) and the Entropy must be converted to kJ by dividing by '1000'/ Hence dG = - 54.32kJ/mol - (327.32K)(-0.3542 kJ/molK) NB The 'K' cancels out. Then maker the multiplication dG = -54/32 kJ/mol - - 115.94 kJ/mol Note the double minus; it becomes plus(+). Hence dG = -54.32kj/mol + 115.94 kJ/mol dG = (+)61.61 kJ/mol Since dG is positive, the reaction is NOT thermodynamically feasible.
The internal energy of a gas is given by the equation U = nCvT, where n is the number of moles, Cv is the molar heat capacity at constant volume, and T is the temperature in Kelvin. For N2 gas, Cv is 20.8 J/(molK). Plugging in the values, U = (4.50 mol) * (20.8 J/(molK)) * (253+273) K. Solving gives you the internal energy.
It is spontaneous.
It is not spontaneous.
The volume can be calculated using the ideal gas law equation, V = (nRT) / P, where n is the number of moles (1.20 mol), R is the gas constant (8.31 LkPa/molK), T is the temperature in Kelvin (25 + 273 = 298 K), and P is the pressure (61.3 kPa). Substituting these values into the equation gives V = (1.20 mol * 8.31 LkPa/molK * 298 K) / 61.3 kPa ≈ 49.1 L.
The internal energy of a gas is given by the equation: U = (3/2) * n * R * T, where n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. For diatomic nitrogen gas (N2), the gas constant is 8.314 J/(molK). Plugging in the values: U = (3/2) * 4.00 mol * 8.314 J/(molK) * 455 K = 55957.76 J.