A party-supply store sells a helium-gas cylinder with a volume of 1.55 × 10^-2 m^3. If the cylinder provides 1.81 m^3 of helium for balloon inflation (at STP), what must be the pressure inside the cylinder?
Now I don't understand this at all. My book does not explain how to do problems like these and I need help. Any takers?
In essence you will place the same number of mols that occupy 1.81 m^3 into a volume of 0.0155 m^3 so the pressure will increase by the inverse of the volumes; i.e.,
1 atm (the initial P) x (1.81/0.0155) = ? atm
Of course! I can help you understand how to solve this problem.
To find the pressure inside the cylinder, 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 moles, R is the ideal gas constant, and T is the temperature in Kelvin.
In this case, we need to find the pressure, and we know the volume of the cylinder (1.55 × 10^-2 m^3), and the volume of helium provided (1.81 m^3).
First, let's convert the volumes to the same units. Since the ideal gas law equation uses SI units, we need to convert the volume of the cylinder to liters by multiplying it by 1000. Hence, the volume of the cylinder is 1.55 × 10^-2 x 1000 = 15.5 liters.
Next, we can rearrange the ideal gas law equation to solve for pressure:
P = (nRT) / V,
Since the problem states that the cylinder provides 1.81 m^3 of helium (at STP), we know the volume (V) of the helium is 1.81 m^3.
Now, we can substitute the given information into the equation. First, we need to determine the number of moles (n) of helium.
At STP (standard temperature and pressure), 1 mole of any ideal gas occupies 22.4 liters. Therefore, to find the number of moles of helium, we can divide the volume of helium by 22.4:
n = V / 22.4,
n = 1.81 / 22.4,
n ≈ 0.08 moles.
Now, we can substitute the values into the equation:
P = (0.08 moles) * (0.0821 L * atm / (mol * K)) * (273 K) / (15.5 L),
P ≈ 0.898 atm.
Therefore, the pressure inside the cylinder should be approximately 0.898 atmospheres (atm).
Of course! I can help you with this problem. To find the pressure inside the cylinder, we can use the ideal gas law formula:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant (8.31 J/(mol·K))
T is the temperature in Kelvin
Since the helium gas is at standard temperature and pressure (STP), we know that the temperature is 273.15 K and the pressure is 1 atmosphere (atm). We are given the volume of helium that the cylinder provides: 1.81 m^3.
First, we need to calculate the number of moles of helium gas using the equation:
n = V / Vm
Where:
n is the number of moles
V is the volume of helium provided (1.81 m^3)
Vm is the molar volume of the gas at STP (22.414 m^3/mol)
Let's calculate the number of moles:
n = 1.81 m^3 / 22.414 m^3/mol
n ≈ 0.08071 mol
Now, we can rearrange the ideal gas law equation to solve for pressure:
P = nRT / V
Plugging in the known values:
n = 0.08071 mol
R = 8.31 J/(mol·K)
T = 273.15 K
V = 1.55 × 10^-2 m^3
P = (0.08071 mol * 8.31 J/(mol·K) * 273.15 K) / (1.55 × 10^-2 m^3)
P ≈ 350,298.48 J/m^3
Since pressure is typically measured in atmospheres (atm), we need to convert J/m^3 to atm:
1 atm = 101,325 J/m^3
P ≈ 350,298.48 J/m^3 / 101,325 J/m^3
P ≈ 3.453 atm
Therefore, the pressure inside the cylinder is approximately 3.453 atmospheres (atm).