A syringe with a movable piston, contains 0.057g of carbon dioxide gas at 23.5C. If the pressure in the syringe was 953mmHg, what would be the volume of the gas in the syringe?
I got 2.59L, but it was wrong.
Do you have any idea how large a volume 2.59 L is? Something like 2.5 quarts.
moles = grams CO2/molar mass CO2. Then use PV = nRT. Don't forget to use Kelvin for T (K = 273 + C). Also, don't forget to convert 953 mm to atmospheres. (953 mm x (1 atm/760 mm = ??).
To calculate the volume of the gas in the syringe, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in atm)
V = volume of the gas (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature of the gas (in Kelvin)
First, let's convert the given pressure from mmHg to atm:
1 atm = 760 mmHg
So, the pressure in terms of atm is 953 mmHg * (1 atm / 760 mmHg) = 1.255 atm.
Now, we need to calculate the number of moles of carbon dioxide (CO2) gas. We can use the molar mass of CO2, which is approximately 44 g/mol.
Number of moles (n) = mass of CO2 / molar mass of CO2
n = 0.057 g / 44 g/mol
n ≈ 0.00130 mol
Next, we need to convert the temperature from Celsius to Kelvin:
Temperature in Kelvin (T) = temperature in Celsius + 273.15
T = 23.5°C + 273.15
T = 296.65 K
Now, we have all the values to substitute into the ideal gas law equation:
(PV) / (nT) = R
Multiplying through by (nT), we get:
PV = nRT
Substituting the known values:
(1.255 atm) * V = (0.00130 mol) * (0.0821 L·atm/(mol·K)) * (296.65 K)
Simplifying the equation:
V = (0.00130 mol) * (0.0821 L·atm/(mol·K)) * (296.65 K) / (1.255 atm)
Calculating the volume:
V ≈ 0.0285 L or 28.5 mL
Therefore, the volume of the gas in the syringe would be approximately 0.0285 L or 28.5 mL, not 2.59 L.