A sample of NH3 gas occupies 75.0 liters at STP. How many molecules is this?
To calculate the number of molecules in a given amount of a gas, we can use Avogadro's law. According to Avogadro's law, one mole of any gas, at standard temperature and pressure (STP), occupies a volume of 22.4 liters.
Given that the sample of NH3 gas occupies 75.0 liters at STP, we can calculate the number of moles of NH3 using the following formula:
Number of moles = Volume / Volume of one mole (at STP)
Number of moles = 75.0 L / 22.4 L/mol
Number of moles ≈ 3.35 mol
To find the number of molecules, we can use Avogadro's number, which states that one mole of any substance contains 6.022 x 10^23 molecules.
Number of molecules = Number of moles x Avogadro's number
Number of molecules ≈ 3.35 mol x (6.022 x 10^23 molecules/mol)
Number of molecules ≈ 2.01 x 10^24 molecules
Therefore, the sample of NH3 gas with a volume of 75.0 liters at STP contains approximately 2.01 x 10^24 molecules.
To determine the number of molecules, you will first need to convert the volume of gas into the number of moles, and then use Avogadro's number to calculate the number of molecules.
STP (Standard Temperature and Pressure) is defined as 1 atmosphere (atm) of pressure and 0 degrees Celsius (0°C) or 273 Kelvin (K).
Step 1: Convert temperature from Celsius to Kelvin.
0°C + 273 = 273 K
Step 2: Use the Ideal Gas Law to calculate the number of moles.
PV = nRT
Given:
Pressure (P) = 1 atmosphere (atm)
Volume (V) = 75.0 liters
Temperature (T) = 273 K
R = 0.0821 L.atm/(mol.K) (Ideal Gas Constant)
Plugging in the values:
(1 atm)(75.0 L) = n(0.0821 L.atm/(mol.K))(273 K)
Dividing both sides by (0.0821 L.atm/(mol.K))(273 K), we can solve for n (number of moles).
n = (1 atm)(75.0 L) / (0.0821 L.atm/(mol.K))(273 K)
Step 3: Calculate the number of molecules using Avogadro's number.
1 mole of any gas at STP contains approximately 6.022 × 10^23 molecules (Avogadro's number).
Using the calculated number of moles from Step 2, multiply it by Avogadro's number to obtain the number of molecules.
Number of molecules = n × (6.022 × 10^23)
Simply substitute the value of n that you obtained from Step 2 into the equation to find out how many molecules of NH3 gas are present in 75.0 liters at STP.