Question

При концентрации газа 1,8 * 10^25 м^-3 и температуре 277°C молекулы газа производят на стенки баллона давление p. Определите значение p. Во сколько раз изменится давление газа при изменении его температуры в 2,5 раза?

Answer 1

Ответ:

в 3,8 раза ответ правилен мне учитель сказал

Answer 2

Calculation of Pressure

To determine the value of pressure (p) exerted by the gas molecules on the walls of the container, we can use the ideal gas law equation:

pV = nRT

Where: - p is the pressure of the gas - 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 in Kelvin

First, let's convert the given temperature from Celsius to Kelvin:

T = 277°C + 273.15 = 550.15 K

Next, we need to calculate the number of moles (n) of gas. To do this, we can use Avogadro's law, which states that one mole of any gas at standard temperature and pressure (STP) occupies a volume of 22.4 liters.

Given that the concentration of the gas is 1.8 * 10^25 m^-3, we can calculate the volume (V) of the gas using the formula:

V = (1 / concentration) * (1 mole / 22.4 liters)

Substituting the given concentration into the formula:

V = (1 / 1.8 * 10^25 m^-3) * (1 mole / 22.4 liters)

Now, let's calculate the value of V:

V = (1 / 1.8 * 10^25) * (1 / 22.4) = 2.78 * 10^-27 liters

Since we have the values of V, n, R, and T, we can rearrange the ideal gas law equation to solve for p:

p = (nRT) / V

Substituting the values into the equation:

p = (n * R * T) / V

Now, let's calculate the value of p:

p = (n * R * T) / V = (n * 0.0821 L * atm / (mol * K) * 550.15 K) / (2.78 * 10^-27 L) = 1.62 * 10^31 atm

Therefore, the value of p is approximately 1.62 * 10^31 atm.

Change in Pressure with Temperature

To determine how the pressure of the gas changes when its temperature is increased by a factor of 2.5, we can use Charles's law, which states that the volume of a gas is directly proportional to its temperature at constant pressure.

Mathematically, Charles's law can be expressed as:

V1 / T1 = V2 / T2

Where: - V1 is the initial volume of the gas - T1 is the initial temperature of the gas - V2 is the final volume of the gas - T2 is the final temperature of the gas

In this case, we are interested in the change in pressure, so we can assume that the volume remains constant. Therefore, the equation becomes:

p1 / T1 = p2 / T2

Let's denote the initial pressure as p1 and the final pressure as p2. We know that the initial temperature (T1) is 550.15 K. To find the final temperature (T2), we multiply the initial temperature by 2.5:

T2 = 2.5 * T1 = 2.5 * 550.15 K = 1375.375 K

Now, we can rearrange the equation to solve for p2:

p2 = (p1 * T2) / T1

Substituting the values into the equation:

p2 = (1.62 * 10^31 atm * 1375.375 K) / 550.15 K = 4.05 * 10^31 atm

Therefore, the pressure of the gas will increase by a factor of approximately 2.5 when its temperature is increased by a factor of 2.5.

Please note that the calculations provided are based on the given information and assumptions.