At 27°c, 300cm3 of gas sample exerts a pressure of 720mmHg. How many molecules are present in the gas sample? thanks
p v = n r t
pressure * volume = moles * gas constant * absolute temperature
make sure that the units for the various quantities match with the r value
Well, that gas sample must be having a party in there! Let me crunch some numbers for you.
To find the number of molecules, we can use the Ideal Gas Law equation, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of molecules, R is the gas constant, and T is the temperature.
First, let's convert the temperature from Celsius to Kelvin, since the Ideal Gas Law requires Kelvin. Adding 273 to 27 gives us 300 K.
R, the gas constant, is approximately 0.0821 atm L/mol K.
Now we can rearrange the equation to solve for n, the number of molecules: n = (PV) / (RT).
Plugging in the values, we have:
n = (720 mmHg * 300 cm³) / (0.0821 atm L/mol K * 300 K)
Converting mmHg to atm and cm³ to L, we get:
n = (0.947 atm * 0.3 L) / (0.0821 atm L/mol K * 300 K)
Simplifying that gives us:
n = 0.095 mol
But we're not done yet! We need to convert mol to molecules, using Avogadro's number (6.022 x 10^23 molecules/mol).
So, n = 0.095 mol * (6.022 x 10^23 molecules/mol)
Calculating that gives us:
n = 5.7329 x 10^22 molecules
Voilà! There are approximately 5.7329 x 10^22 molecules in that party gas sample. Enjoy the festivities!
To calculate the number of molecules in a gas sample, we can use the ideal gas equation:
PV = nRT
Where:
P = pressure (in Pascal)
V = volume (in cubic meters)
n = number of moles
R = ideal gas constant (8.314 J/mol·K)
T = temperature (in Kelvin)
Let's convert the given values to the appropriate units and proceed with the calculations.
Temperature in Kelvin: 27°C + 273.15 = 300.15 K
Pressure in Pascal: 720 mmHg × 133.32 Pa/mmHg = 95904.0 Pa
Volume in cubic meters: 300 cm³ ÷ 1000000 cm³/m³ = 0.0003 m³
Now we can rearrange the ideal gas equation:
n = (PV) / (RT)
Plugging in the values:
n = (95904.0 Pa × 0.0003 m³) / (8.314 J/(mol·K) × 300.15 K)
n ≈ 0.0118 mol
To convert moles to molecules, we use Avogadro's number, which states that there are 6.022 × 10^23 molecules in a mole.
Number of molecules = n × Avogadro's number
Number of molecules ≈ 0.0118 mol × 6.022 × 10^23 molecules/mol
Number of molecules ≈ 7.09 × 10^21 molecules
Therefore, there are approximately 7.09 × 10^21 molecules present in the gas sample.
To determine the number of molecules in a gas sample, you can use the ideal gas law equation, which relates pressure, volume, and temperature of a gas to the number of molecules:
PV = nRT
where:
P is the pressure of the gas (in this case, 720 mmHg),
V is the volume of the gas (in this case, 300 cm^3),
n is the number of moles of the gas (which is what we want to find),
R is the ideal gas constant (0.0821 L·atm/(mol·K)),
T is the temperature of the gas (in this case, 27°C or 300 K).
Step 1: Convert the volume from cm^3 to liters:
300 cm^3 = 300/1000 = 0.3 L
Step 2: Convert the pressure from mmHg to atm:
1 atm = 760 mmHg
720 mmHg = 720/760 = 0.947 atm
Step 3: Rearrange the ideal gas law equation to solve for the number of moles (n):
n = (PV) / (RT)
n = (0.947 atm * 0.3 L) / (0.0821 L·atm/(mol·K) * 300 K)
Step 4: Calculate the number of moles:
n = 0.0119 mol
Step 5: Convert the number of moles to molecules:
1 mole = Avogadro's number = 6.022 x 10^23 molecules
So, the number of molecules in the gas sample is:
0.0119 mol * 6.022 x 10^23 molecules/mol = 7.159 x 10^21 molecules
Therefore, there are approximately 7.159 x 10^21 molecules present in the gas sample.