Question

В герметическом сосуде вместимостью 4 л заполненном предварительно при нормальных условиях кислородом , сожгли 5,6г кальция. образовавшееся соединение (оксид) находится в твердом виде и его обьемом можно принебречь. расчитайте температуру газа в сосуде , если известно что после реакции давление в сосуде 120,4 кПа

Answer 1

Ca + 0.5O2 = CaO;

n исх. O2 = 101.3*4/(8.314*273) = 0.178524 моль;

n O2 в р-ии = (5.6/40)*0.5 = 0.07 моль;

т.о. после р-ии ост-я 0.178524-0.07 = 0.108524 моль O2;

T = 120.4*4/(0.108524*8.314) = 533.766 K или 260.766 C.

Answer 2

Calculation of Gas Temperature in the Sealed Vessel

To calculate the temperature of the gas in the sealed vessel after the reaction, we can use the ideal gas law equation:

PV = nRT

Where: - P is the pressure of the gas (given as 120.4 kPa) - V is the volume of the gas (given as 4 L) - n is the number of moles of gas (to be determined) - R is the ideal gas constant (8.314 J/(mol·K)) - T is the temperature of the gas (to be determined)

First, we need to determine the number of moles of gas present in the vessel. We can use the molar mass of calcium (Ca) to calculate the number of moles of calcium consumed in the reaction.

The molar mass of calcium (Ca) is approximately 40.08 g/mol.

Given that 5.6 g of calcium was consumed in the reaction, we can calculate the number of moles of calcium:

moles of calcium = mass of calcium / molar mass of calcium

moles of calcium = 5.6 g / 40.08 g/mol

Now, we need to determine the number of moles of oxygen (O2) consumed in the reaction. The reaction between calcium and oxygen forms calcium oxide (CaO), and the balanced chemical equation is:

2Ca + O2 → 2CaO

From the balanced equation, we can see that 2 moles of calcium react with 1 mole of oxygen to form 2 moles of calcium oxide.

Therefore, the number of moles of oxygen consumed is half the number of moles of calcium consumed:

moles of oxygen = moles of calcium / 2

Now that we know the number of moles of oxygen, we can calculate the total number of moles of gas present in the vessel:

total moles of gas = moles of calcium + moles of oxygen

Finally, we can rearrange the ideal gas law equation to solve for the temperature (T):

T = (PV) / (nR)

Substituting the given values, we can calculate the temperature of the gas in the vessel.

Please note that the volume of the solid compound formed (calcium oxide) can be neglected, as mentioned in the question.

Let's perform the calculations.

Calculation:

1. Calculate the number of moles of calcium: - Molar mass of calcium (Ca) = 40.08 g/mol - Moles of calcium = 5.6 g / 40.08 g/mol

2. Calculate the number of moles of oxygen: - Moles of oxygen = Moles of calcium / 2

3. Calculate the total moles of gas: - Total moles of gas = Moles of calcium + Moles of oxygen

4. Calculate the temperature of the gas using the ideal gas law equation: - Temperature (T) = (Pressure (P) * Volume (V)) / (Total moles of gas * Ideal gas constant (R))

Let's perform the calculations step by step.

Step 1: Calculate the number of moles of calcium:

Molar mass of calcium (Ca) = 40.08 g/mol

Moles of calcium = 5.6 g / 40.08 g/mol

Step 2: Calculate the number of moles of oxygen:

Moles of oxygen = Moles of calcium / 2

Step 3: Calculate the total moles of gas:

Total moles of gas = Moles of calcium + Moles of oxygen

Step 4: Calculate the temperature of the gas using the ideal gas law equation:

Temperature (T) = (Pressure (P) * Volume (V)) / (Total moles of gas * Ideal gas constant (R))

Now, let's perform the calculations.

Calculation:

Step 1: Calculate the number of moles of calcium: - Molar mass of calcium (Ca) = 40.08 g/mol - Moles of calcium = 5.6 g / 40.08 g/mol

Moles of calcium = 0.1396 mol

Step 2: Calculate the number of moles of oxygen: - Moles of oxygen = Moles of calcium / 2

Moles of oxygen = 0.1396 mol / 2

Moles of oxygen = 0.0698 mol

Step 3: Calculate the total moles of gas: - Total moles of gas = Moles of calcium + Moles of oxygen

Total moles of gas = 0.1396 mol + 0.0698 mol

Total moles of gas = 0.2094 mol

Step 4: Calculate the temperature of the gas using the ideal gas law equation: - Pressure (P) = 120.4 kPa - Volume (V) = 4 L - Total moles of gas = 0.2094 mol - Ideal gas constant (R) = 8.314 J/(mol·K)

Temperature (T) = (Pressure (P) * Volume (V)) / (Total moles of gas * Ideal gas constant (R))

Temperature (T) = (120.4 kPa * 4 L) / (0.2094 mol * 8.314 J/(mol·K))

Temperature (T) = 2303.36 kJ / (1.738 kJ/K)

Temperature (T) ≈ 1325.3 K

Therefore, the temperature of the gas in the sealed vessel is approximately 1325.3 Kelvin (K).

Please note that the temperature is given in Kelvin (K), which is the SI unit for temperature.