Question

В сосуде объемом 1 л заключено 0,28 г азота. Азот нагрет до температуры 1500 °С. При этой тем¬пературе 30% молекул азота диссоциировало на атомы. Определить давление в сосуде.

Answer 1

N - число молекул в сосуде до начала диссоциации.

Тогда N = $N_{A}$m/M, где $N_{A}$  - число Авогадро, M - молекулярная масса азота. 
Раз 30% молекул диссоциировали на атомы, то понятно, что число молекул в сосуде изменилось. Теперь в сосуде находятся молекулы в количестве 0,7·N и атомы, число которых равно 0,6 ·N. Парциальное давление газа равно $P_{1}$ = 0,7kTN/V, где k - постоянная Больцмана, T - абсолютная температура, а давление атомов равно $P_{2}$  = 0,6kTN/V. 

Полное давление на стенки сосуда определяется суммой этих давлений
P = $P_{1}$ + $P_{2}$ = 1,3RTm/(MV) 

 

Подставляем данные, и вуаля!

 

Ответ:$1,92*10^{5}$ Па

Answer 2

Calculation of Pressure in the Vessel

To determine the pressure in the vessel, we can use the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature and the number of moles of gas present, and inversely proportional to the volume of the container.

The ideal gas law equation is given by:

PV = nRT

Where: - P is the pressure of the gas - V is the volume of the container - n is the number of moles of gas - R is the ideal gas constant - T is the temperature of the gas in Kelvin

In this case, we are given: - Volume of the vessel (V) = 1 L - Mass of nitrogen (m) = 0.28 g - Temperature of nitrogen (T) = 1500 °C - Percentage of nitrogen molecules that dissociated (d) = 30%

To calculate the number of moles of nitrogen (n), we need to convert the mass of nitrogen to moles using the molar mass of nitrogen.

The molar mass of nitrogen (N₂) is approximately 28 g/mol.

n = m / M

Where: - m is the mass of nitrogen - M is the molar mass of nitrogen

Let's calculate the number of moles of nitrogen:

n = 0.28 g / 28 g/mol = 0.01 mol

Now, we need to calculate the number of moles of nitrogen that dissociated (n_dissociated) based on the percentage of dissociation (d).

n_dissociated = n * d / 100

Let's calculate the number of moles of dissociated nitrogen:

n_dissociated = 0.01 mol * 30 / 100 = 0.003 mol

The remaining moles of nitrogen (n_remaining) can be calculated by subtracting the moles of dissociated nitrogen from the total moles of nitrogen.

n_remaining = n - n_dissociated

n_remaining = 0.01 mol - 0.003 mol = 0.007 mol

Now, we can calculate the pressure (P) using the ideal gas law equation:

P = n_remaining * R * T / V

Where: - R is the ideal gas constant, which is approximately 0.0821 L·atm/(mol·K)

Let's calculate the pressure in the vessel:

P = 0.007 mol * 0.0821 L·atm/(mol·K) * (1500 + 273) K / 1 L

Calculating this expression gives us the pressure in the vessel.

Please note that the temperature needs to be converted to Kelvin by adding 273 to the given temperature in Celsius.