Question

В закрытой бутылке под давлением находится 10 моль газа. Бутылку вносят в комнату с площадью S=30 м² и высотой h=3 м и открывают. Молярная масса газа 48 г/моль. Найдите концентрацию n молекул в-ва в комнате после того, как оно разойдется по всему объему. Какова масса одной молекулы этого газа?

Answer 1

Calculation of Gas Concentration in the Room

To find the concentration of the gas in the room after it has dispersed throughout the entire volume, we need to calculate the number of moles of gas and then convert it to the number of molecules.

Given: - Amount of gas in the bottle (n): 10 moles - Molar mass of the gas (M): 48 g/mol - Room area (S): 30 m² - Room height (h): 3 m

To calculate the concentration of the gas in the room, we can use the ideal gas law:

PV = nRT

Where: - P is the pressure of the gas (which is assumed to be constant) - V is the volume of the gas - n is the number of moles of gas - R is the ideal gas constant - T is the temperature of the gas (which is assumed to be constant)

Since the gas is released into the room, it will occupy the entire volume of the room. The volume of the room can be calculated by multiplying the area of the room by its height:

V = S * h

Substituting this into the ideal gas law equation, we get:

P * S * h = n * R * T

We can rearrange this equation to solve for the concentration of the gas (n/V):

n/V = P / (R * T / (S * h))

Now we can calculate the concentration of the gas in the room.

Using the given values: - P (pressure) is not provided, so we cannot calculate the exact concentration without this information. - R (ideal gas constant) is approximately 8.31 J/(mol·K). - T (temperature) is not provided, so we cannot calculate the exact concentration without this information.

Without the values for pressure (P) and temperature (T), we cannot determine the exact concentration of the gas in the room.

Calculation of the Mass of One Molecule of the Gas

To calculate the mass of one molecule of the gas, we need to know the molar mass of the gas and Avogadro's number.

Given: - Molar mass of the gas (M): 48 g/mol

Avogadro's number (N_A) is approximately 6.022 x 10^23 molecules/mol.

To calculate the mass of one molecule of the gas, we can use the formula:

Mass of one molecule = Molar mass / Avogadro's number

Substituting the given values, we get:

Mass of one molecule = 48 g/mol / (6.022 x 10^23 molecules/mol)

Calculating this, we find that the mass of one molecule of the gas is approximately 7.98 x 10^-23 grams.

Please note that the calculation of the mass of one molecule assumes that the molar mass provided is the mass of one mole of the gas. If the molar mass is given as the mass of one molecule, the calculation would be different.