gas law stoichiometry

Question

If a 0.154 g block of sodium is placed in excess water, heat and a gas are produced. If the gas is at STP, how many milliliters of gas are produced?

Answer 1

Sodium (Na) plus water (H₂O) produces sodium hydroxide (NaOH) and hydrogen gas (H₂) so the unbalanced chemical reaction equation is:

Na + H₂O → NaOH + H₂

Balancing it gives:

2Na + 2H₂O → 2NaOH + H₂

0.154 g of sodium is converted to moles by dividing by the molar mass of sodium (found on the perioding table) as 22.99 g/mol

0.154/22.99 = 0.0066986 moles

In looking at the balanced chemical reaction equation, there are 2 moles of Na needed for each mole of H₂ produced so that means the moles of H₂ produced is 0.0066986/2 = 0.003349 moles

Where are asked to find volume (milliliters) so, since the Ideal Gas Law is PV = nRT we can say:

V = nRT/P

Since we are told the gas is at STP, that means T = 273.15 K and P = 1 atm. The value of R (the Ideal Gas Constant) in units of L•atm/K/mol is 0.082057. Note that we will get an answer then in liters so we will need to convert that answer to milliliters before finishing.

V = (0.003349)(0.082057)(273.15)/(1) = 0.07507 liters. Since there are 1000 mL in 1 liter, we multiply by 1000 to get V = 75.1 mL