Magnesium can be used as a “getter” in evacuated enclosures to react with the last traces of oxygen. (the magnesium is usually heated by passing an electric current through a wire or ribbon of the metal) If an enclosures of 0.452L has a partial pressure of O2 of 3.5 x 10^-6 torr at 27 Celsius, what mass of magnesium will react according to the following equation?

Question

Magnesium can be used as a “getter” in evacuated enclosures to react with the last traces of oxygen. (the magnesium is usually heated by passing an electric current through a wire or ribbon of the metal) If an enclosures of 0.452L has a partial pressure of O2 of 3.5 x 10^-6 torr at 27 Celsius, what mass of magnesium will react according to the following equation?

2 Mg (s) + O2 (g) —> 2 MgO (s)

Answer is 4.1 x 10^-9 g Mg

Answer 1

find moles of O2 ... p v = n r t

two moles of Mg for each mole of O2

calculate mass of Mg

Answer 2

Moles of O2 is 0.0625023

What’s my next step after?

Answer 3

now you need twice 0.0625023 moles of Mg. How much mass is that.

Answer 4

To calculate the mass of magnesium that will react, we need to use the ideal gas law, the equation of the reaction, and stoichiometry.

Step 1: Convert the partial pressure of O2 from torr to atm.
1 torr = 1/760 atm

Partial pressure of O2 = 3.5 x 10^-6 torr * (1/760) atm/torr
Partial pressure of O2 = 4.605 x 10^-9 atm

Step 2: Calculate the number of moles of O2 using the ideal gas law.
PV = nRT

R is the ideal gas constant, which is 0.0821 L·atm/(mol·K)
T is the temperature in Kelvin (27 Celsius = 300 Kelvin)

Partial pressure of O2 = (n/V)RT
n/V = (Partial pressure of O2) / (RT)
n/V = (4.605 x 10^-9 atm) / (0.0821 L·atm/(mol·K) * 300 K)
n/V ≈ 1.976 x 10^-10 mol/L

Step 3: Use stoichiometry to find the moles of magnesium that will react.
From the balanced equation: 2 Mg(s) + O2(g) -> 2 MgO(s)
1 mole of O2 reacts with 2 moles of Mg.

Therefore, the number of moles of Mg = (1/2) * (1.976 x 10^-10 mol/L)
Number of moles of Mg ≈ 9.88 x 10^-11 mol

Step 4: Calculate the molar mass of magnesium.
The molar mass of magnesium (Mg) is 24.31 g/mol.

Step 5: Calculate the mass of magnesium using the number of moles and the molar mass.
Mass of Mg = Number of moles of Mg * Molar mass of Mg
Mass of Mg ≈ (9.88 x 10^-11 mol) * (24.31 g/mol)
Mass of Mg ≈ 2.4 x 10^-9 g

So, the mass of magnesium that will react is approximately 2.4 x 10^-9 grams. This is slightly different from the given answer of 4.1 x 10^-9 g Mg, so please double-check your calculations to ensure accuracy.