Question

Question from "old is gold." Calculate the number of moles of molecules present in 50 mL of an ideal gas entering a pressure of 770 mmHg at 25°C (R = 0.0821 atm mol^-1 K^-1).

Answer 1

To calculate the number of moles of molecules in 50 mL of an ideal gas, use the ideal gas law equation. Convert the given volume to liters, then substitute the values into the equation. Solve for n, which represents the number of moles.

Step-by-step explanation:

To calculate the number of moles of molecules present in 50 mL of an ideal gas, we need to use the ideal gas law equation, PV = nRT. In this equation, P represents the pressure, V represents the volume, n represents the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

1. First, we need to convert the given volume from milliliters to liters. Since 1 L = 1000 mL, 50 mL is equal to 0.05 L.
2. Next, we substitute the given values into the ideal gas law equation. P is given as 770 mmHg, which can be converted to atm by dividing by 760 (since 1 atm = 760 mmHg). So, P = 770 mmHg ÷ 760 = 1.0132 atm. R is given as 0.0821 atm mol^-1 K^-1.
3. Plugging in the values, we get (1.0132 atm) (0.05 L) = n (0.0821 atm mol^-1 K^-1) (298 K).
4. Solving for n, we find n = 0.00209 mol.

Therefore, there are approximately 0.00209 moles of molecules present in 50 mL of the ideal gas.