how many molecules of N2 could fit in a 2.00L soda bottle at 23C and 755mmHg

Set up: convert units --> PV=nRT --> PV/RT=n --> moles to molecules.

(0.993atm*2.00L)/(0.08206*296.15K)=0.08176 mol N2

0.08176 mol*(6.022x10^23 molecules/1 mol)=4.92x10^22 molecules N2

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To determine the number of molecules of N2 that could fit in a 2.00L soda bottle, 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)

First, we need to convert the temperature from Celsius to Kelvin:
T(Kelvin) = T(Celsius) + 273.15
T(Kelvin) = 23 + 273.15 = 296.15 K

Next, we need to convert the pressure from mmHg to atm:
P(atm) = P(mmHg) / 760 mmHg/atm
P(atm) = 755 mmHg / 760 mmHg/atm = 0.9934 atm

Now we can rearrange the ideal gas law equation to solve for the number of moles:
n = PV / RT

n = (0.9934 atm) * (2.00 L) / ((0.0821 L·atm/mol·K) * (296.15 K))

Simplifying the equation, we get:
n ≈ 0.0844 mol

Finally, we can convert moles to molecules using Avogadro's number (6.022 x 10^23 molecules/mol):
Number of molecules = n * (6.022 x 10^23 molecules/mol)
Number of molecules ≈ 0.0844 mol * (6.022 x 10^23 molecules/mol)

Therefore, the number of molecules of N2 that could fit in a 2.00L soda bottle at 23°C and 755 mmHg is approximately 5.08 x 10^22 molecules.

To determine the number of molecules of N2 that can fit in a 2.00L soda bottle at 23°C and 755 mmHg, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure (in units of force per unit area)
V = volume (in units of cubic meters)
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)

First, we need to convert the given temperature of 23°C to Kelvin (K) by adding 273.15:
T = 23°C + 273.15 = 296.15 K

Next, convert the pressure from mmHg to atmospheres (atm):
1 atm = 760 mmHg
755 mmHg / 760 mmHg = 0.9934 atm

Now, we can rearrange the ideal gas law equation to solve for the number of moles (n):

n = PV / RT

Substituting the known values:
n = (0.9934 atm) * (2.00 L) / [(8.314 J/(mol·K)) * (296.15 K)]

Calculating:
n ≈ 0.000137 mol

Finally, using Avogadro's number, which states that 1 mole of any substance contains 6.022 x 10^23 molecules, we can find the number of molecules of N2 that can fit in the 2.00L soda bottle:

Number of molecules = n * Avogadro's number
Number of molecules ≈ (0.000137 mol) * (6.022 x 10^23 molecules/mol)

Calculating:
Number of molecules ≈ 8.25 x 10^19 molecules

Therefore, approximately 8.25 x 10^19 molecules of N2 can fit in the 2.00L soda bottle at 23°C and 755 mmHg.