Question

A sample of He at 25C and 755 torr occupies a fixed volume of 16.8L. What mass of He must be pumped in to increase the pressure to 1.87 atm if the temperature remains the same?

Answer 1

2.4 g

Step-by-step explanation:

Step 1: Given data

• Initial pressure (P₁): 755 torr

• Volume (V): 16.8 L

• Temperature (T): 25 °C

• Final pressure (P₂): 1.87 atm

Step 2: Convert "P₁" to atm

We will use the conversion factor 1 atm = 760 torr.

755 torr × 1 atm/760 torr = 0.993 atm

Step 3: Convert "T" to K

We will use the following expression.

K = °C + 273.15

K = 25°C + 273.15 = 298 K

Step 4: Calculate the initial number of moles of He

We will use the ideal gas equation.

P₁ × V = n₁ × R × T

n₁ = P₁ × V/R × T

n₁ = 0.993 atm × 16.8 L/(0.0821 atm.L/mol.K) × 298 K

n₁ = 0.682 mol

Step 5: Calculate the final number of moles of He

We will use the ideal gas equation.

P₂ × V = n₂ × R × T

n₂ = P₂ × V/R × T

n₂ = 1.87 atm × 16.8 L/(0.0821 atm.L/mol.K) × 298 K

n₂ = 1.28 mol

Step 6: Calculate the moles of He added

n = n₂ - n₁

n = 1.28 mol - 0.682 mol

n = 0.60 mol

Step 7: Convert "n" to mass

The molar mass of He is 4.00 g/mol

0.60 mol × 4.00 g/mol = 2.4 g