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25cm³ of a gas x contains z molecules at 15 census and 75mmhg how many molecules will 25 cm³ of another gas y contain at the same temperature and pressure??

Mar 18

Chemistry

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Mar 18

To solve this problem, we can use the ideal gas law equation:

PV = nRT

Where:

P = pressure

V = volume

n = number of moles

R = ideal gas constant

T = temperature

Since we are comparing two gases at the same temperature and pressure, we can set up a ratio of the number of molecules in gas x to the number of molecules in gas y:

n_x / n_y = z_x / z_y

Given that the volume and temperature are the same for both gases, we can simplify the equation to:

n_x / n_y = z_x / z_y

Since the volume and temperature are the same for both gases, the ratio of the number of molecules in gas x to the number of molecules in gas y is equal to the ratio of the number of molecules in gas x to the number of molecules in gas y.

Therefore, the number of molecules in gas y can be calculated as:

z_y = (z_x * n_y) / n_x

Given that 25 cm³ of gas x contains z molecules at 15°C and 75 mmHg, we can calculate the number of molecules in gas x:

n_x = PV / RT

n_x = (75 mmHg * 25 cm³) / (0.0821 L atm / mol K * 288 K)

n_x = 0.82 moles

Now we can calculate the number of molecules in gas y:

z_y = (z_x * n_y) / n_x

z_y = (z_x * n_y) / 0.82

Therefore, we need to know the number of molecules in gas y (z_y) to calculate the number of molecules in gas y.

PV = nRT

Where:

P = pressure

V = volume

n = number of moles

R = ideal gas constant

T = temperature

Since we are comparing two gases at the same temperature and pressure, we can set up a ratio of the number of molecules in gas x to the number of molecules in gas y:

n_x / n_y = z_x / z_y

Given that the volume and temperature are the same for both gases, we can simplify the equation to:

n_x / n_y = z_x / z_y

Since the volume and temperature are the same for both gases, the ratio of the number of molecules in gas x to the number of molecules in gas y is equal to the ratio of the number of molecules in gas x to the number of molecules in gas y.

Therefore, the number of molecules in gas y can be calculated as:

z_y = (z_x * n_y) / n_x

Given that 25 cm³ of gas x contains z molecules at 15°C and 75 mmHg, we can calculate the number of molecules in gas x:

n_x = PV / RT

n_x = (75 mmHg * 25 cm³) / (0.0821 L atm / mol K * 288 K)

n_x = 0.82 moles

Now we can calculate the number of molecules in gas y:

z_y = (z_x * n_y) / n_x

z_y = (z_x * n_y) / 0.82

Therefore, we need to know the number of molecules in gas y (z_y) to calculate the number of molecules in gas y.