Question

How many molecules would there be in 10.5L of carbon dioxide at 40.0°C and 2.25 bar? (Use Avogadro's number)

A) Approximately 1.20 x 10^24 molecules
B) Approximately 6.02 x 10^23 molecules
C) Approximately 2.40 x 10^23 molecules
D) Approximately 1.00 x 10^22 molecules

Answer 1

To find the number of molecules in 10.5L of carbon dioxide at 40.0°C and 2.25 bar, we need to use the ideal gas law equation, PV = nRT. Firstly, we need to convert the volume from liters to cubic meters, so the volume becomes 0.0105 m³. Next, we can use Avogadro's number (6.022 × 10^23 molecules/mol) to calculate the number of moles. Rearranging the ideal gas law equation to solve for moles, we have n = PV/RT. Plugging in the given values and solving for n gives us: n = (2.25 bar) * (0.0105 m³) / (0.0821 L·atm/(mol·K) * (40.0 + 273.15) K) ≈ 0.01167 mol. Finally, we can use Avogadro's number to calculate the number of molecules: Number of molecules = (0.01167 mol) * (6.022 × 10^23 molecules/mol) ≈ 7.02 × 10^21 molecules.

Step-by-step explanation:

To find the number of molecules in 10.5L of carbon dioxide at 40.0°C and 2.25 bar, we need to use the ideal gas law equation, PV = nRT. Firstly, we need to convert the volume from liters to cubic meters, so the volume becomes 0.0105 m³. Next, we can use Avogadro's number (6.022 × 10^23 molecules/mol) to calculate the number of moles. Rearranging the ideal gas law equation to solve for moles, we have n = PV/RT. Plugging in the given values and solving for n gives us:

n = (2.25 bar) * (0.0105 m³) / (0.0821 L·atm/(mol·K) * (40.0 + 273.15) K) ≈ 0.01167 mol

Finally, we can use Avogadro's number to calculate the number of molecules:

Number of molecules = (0.01167 mol) * (6.022 × 10^23 molecules/mol) ≈ 7.02 × 10^21 molecules