A chemist is preparing to carry out a reaction at high pressure that requires 36.0 mol of hydrogen gas. The chemist pumps the hydrogen into a 15.5L rigid steel container at 25 degrees Celcius. To what pressure (in atmospheres) must the hydrogen be compressed? What would be the density of the high-pressure hydrogen?
PV=nRT calculate P
density=moles*molmassH2/volume
thank you so much!
To find the pressure to which the hydrogen must be compressed, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atmospheres
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
First, let's convert the temperature from degrees Celsius to Kelvin. We add 273.15 to the Celsius temperature to get:
25°C + 273.15 = 298.15 K
Now we can plug in the values into the ideal gas law equation:
P * 15.5L = 36.0 mol * 0.0821 L·atm/(mol·K) * 298.15 K
P * 15.5L = 36.0 mol * 24.486 L·atm/(mol·K)
P = (36.0 mol * 24.486 L·atm/(mol·K)) / 15.5L
P = 56.37 atm
So, the hydrogen must be compressed to approximately 56.37 atmospheres.
To find the density of the high-pressure hydrogen, we can use the ideal gas law rearranged to solve for density:
PV = nRT
n/V = P/RT
The density (D) is equal to the number of moles (n) divided by the volume (V):
D = n / V
Substituting n/V with P/RT:
D = P / RT
Now we can plug in the values:
D = (56.37 atm) / (0.0821 L·atm/(mol·K) * 298.15 K)
D = 2.48 moles/L
Therefore, the density of the high-pressure hydrogen is approximately 2.48 moles/L.
To find the pressure (P) in atmospheres (atm) to which the hydrogen gas must be compressed, we can use the ideal gas law equation:
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.
Let's break down the given information:
Number of moles of hydrogen gas: n = 36.0 mol
Volume of the container: V = 15.5 L
Temperature in Celsius: T = 25 degrees Celsius
First, we need to convert the temperature from Celsius to Kelvin:
T (Kelvin) = T (Celsius) + 273.15
T (Kelvin) = 25 + 273.15
T (Kelvin) = 298.15 K
Now, we can rearrange the ideal gas law equation to solve for P:
P = nRT / V
Plug in the known values:
P = (36.0 mol) * (0.0821 L*atm/mol*K) * (298.15 K) / (15.5 L)
Simplify:
P = 89.88 atm
Therefore, the hydrogen gas must be compressed to a pressure of approximately 89.88 atmospheres.
To find the density (ρ) of the high-pressure hydrogen, we can use the formula:
ρ = (molar mass) * (pressure) / (gas constant * temperature)
The molar mass of hydrogen (H2) is approximately 2.016 g/mol.
Plugging in the known values:
ρ = (2.016 g/mol) * (89.88 atm) / (0.0821 L*atm/mol*K * 298.15 K)
Simplify:
ρ ≈ 0.0821 g/L
Therefore, the density of the high-pressure hydrogen is approximately 0.0821 g/L.