Gas is contained in a 6.00-L vessel at a temperature of 15.0°C and a pressure of 6.00 atm.
(a) Determine the number of moles of gas in the vessel.
(b) How many molecules are in the vessel?
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To determine the number of moles of gas in the vessel, we can use the ideal gas equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
(a) To find the number of moles, we need to convert the temperature from Celsius to Kelvin. The Kelvin temperature can be found by adding 273.15 to the Celsius temperature.
Given:
V = 6.00 L
T = 15.0°C + 273.15 = 288.15 K
P = 6.00 atm
Next, we can rearrange the ideal gas equation to solve for n:
n = PV / RT
Substituting the values into the equation, we get:
n = (6.00 atm * 6.00 L) / (0.0821 L·atm/(mol·K) * 288.15 K)
Evaluating the expression gives us:
n ≈ 0.148 moles
Therefore, the number of moles of gas in the vessel is approximately 0.148 moles.
(b) To determine the number of molecules, we can use Avogadro's number, which states that 1 mole of any substance contains 6.022 x 10^23 molecules.
Given the number of moles from part (a), we can calculate the number of molecules:
Number of molecules = Number of moles * Avogadro's number
Number of molecules ≈ 0.148 moles * 6.022 x 10^23 molecules/mole
Evaluating the expression gives us:
Number of molecules ≈ 8.89 x 10^22 molecules
Therefore, there are approximately 8.89 x 10^22 molecules in the vessel.