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.