Question

how much hydrogen gas is necessary to exert a pressure of 1.4 ATM at 430k if occupying a volume of 15.1 l

Answer 1

0.60 mol H₂

General Formula and Concepts:

Chemistry - Gas Laws

Ideal Gas Law: PV = nRT

• P is pressure
• V is volume in Liters
• n is number of moles
• R is the gas constant
  `0.0821 (L \cdot atm)/(mol \cdot K)`
• T is temperature in Kelvins

Step-by-step explanation:

Step 1: Define Variables

P = 1.4 atm

T = 430 K

R = 0.0821 (L · atm)/(mol · K)

V = 15.1 L

n = unknown

Step 2: Solve for n

1. Substitute:
   `(1.4 \ atm)(15.1 \ L)=n(0.0821 \ (L \cdot atm)/(mol \cdot K))(430 \ K)`
2. Isolate n:
   `((1.4 \ atm)(15.1 \ L))/((0.0821 \ (L \cdot atm)/(mol \cdot K))(430 \ K) )=n`
3. Multiply:
   `(21.14 \ L \cdot atm)/(35.303\ (L \cdot atm)/(mol) )=n`
4. Divide:
   `0.598816 \ mol =n_(H_2)`
5. Rewrite:
   `n_(H_2) = 0.598816 \ mol`

Step 3: Check

We are given 2 sig figs as our lowest. Follow sig fig rules and round.

0.598816 mol H₂ ≈ 0.60 mol H₂