a 1,000 ml coke bottle is 1/3rd filled with coke, and the rest occupied with air. Suppose this bottle is left outside and allowed to heat up to 120 degrees Fahrenheit. Assuming this bottle has an internal pressure of 768 mmHg how many atoms of gas are inside this container.
Would you use the ideal gas equation of PV=nrt and solve for n.
Yes, you are correct! To find the number of gas atoms inside the container, we can use the ideal gas equation PV = nRT, where P is the pressure, V is the volume, n is the number of gas molecules (or atoms), R is the ideal gas constant, and T is the temperature in Kelvin.
Before we can apply the ideal gas equation, we need to convert the given temperature of 120 degrees Fahrenheit to Kelvin. The conversion formula is:
T(K) = (T(°F) - 32) * (5/9) + 273.15
Let's calculate the temperature in Kelvin:
T(K) = (120 - 32) * (5/9) + 273.15
T(K) = 48 * (5/9) + 273.15
T(K) = 267.15 + 273.15
T(K) = 540.3 K
Now let's plug in the values into the ideal gas equation and solve for n:
PV = nRT
Here are the known values:
P = 768 mmHg
V = 1000 mL (or 1 L)
R = 0.0821 L·atm/(mol·K) (the ideal gas constant)
T = 540.3 K
To make the units consistent, we need to convert the pressure from mmHg to atm:
1 atm = 760 mmHg
P(atm) = 768 mmHg / 760 mmHg
P(atm) = 1.01 atm
Now we can solve for n:
n = (PV) / (RT)
n = (1.01 atm * 1 L) / (0.0821 L·atm/(mol·K) * 540.3 K)
n = 0.0119 mol
To convert moles to the number of atoms, we need to multiply by Avogadro's number (6.022 x 10^23 atoms/mol):
Number of atoms = 0.0119 mol * (6.022 x 10^23 atoms/mol)
Number of atoms ≈ 7.16 x 10^21 atoms
Therefore, there are approximately 7.16 x 10^21 gas atoms inside the container.