To determine the volume that will contain a given number of atoms at STP (Standard Temperature and Pressure), we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
At STP, the temperature is 273.15 Kelvin, and the pressure is 1 atmosphere.
To find the volume, we need to convert the number of neon atoms to moles:
Number of moles (n) = Number of atoms / Avogadro's number
Avogadro's number is approximately 6.022 × 10^23 mol^-1.
Let's calculate the volume using the given information:
Number of atoms = 1.21 × 10^21
Number of moles (n) = (1.21 × 10^21) / (6.022 × 10^23)
Temperature (T) = 273.15 Kelvin
Pressure (P) = 1 atmosphere
Ideal gas constant (R) = 0.0821 L·atm/(mol·K)
Now, we can rearrange the ideal gas law equation to solve for volume (V):
V = (nRT) / P
Let's substitute the values into the equation and calculate the volume:
V = [(1.21 × 10^21) / (6.022 × 10^23)] × (0.0821) × (273.15) / (1)
After performing the calculation, the volume would be approximately equal to 2.05 liters.