Question

Some commercial drain cleaners use a mixture of sodium hydroxide and aluminum

powder. When the solid mixture is poured into the drain and dissolves, a reaction
ensues that produces hydrogen gas:
2NaOH(aq) + 2Al(s) + 6H₂O(→ 2NaAl(OH)4(aq) + 3H₂(g)
Determine the temperature (in °C) of hydrogen gas produced when 26.72 g of
aluminum reacts with excess sodium hydroxide and water if the pressure is 111.42
kPa and the volume is 57.09 L. Provide your answer with TWO decimals.

Answer 1

To determine the temperature of the hydrogen gas produced, we can use the Ideal Gas Law equation:

PV = nRT

Where:

P = pressure (in kPa)

V = volume (in L)

n = number of moles of gas

R = ideal gas constant (8.314 J/(mol·K))

T = temperature (in K)

First, let's calculate the number of moles of hydrogen gas produced:

From the balanced chemical equation, we can see that 2 moles of aluminum react to produce 3 moles of hydrogen gas. Therefore, we need to convert the mass of aluminum (26.72 g) to moles.

The molar mass of aluminum is 26.98 g/mol, so:

Number of moles of aluminum = mass of aluminum / molar mass of aluminum

= 26.72 g / 26.98 g/mol

≈ 0.990 moles

Since the reaction produces a 2:3 ratio of aluminum to hydrogen gas, the number of moles of hydrogen gas produced would be:

Number of moles of hydrogen gas = (3/2) * number of moles of aluminum

= (3/2) * 0.990 moles

≈ 1.485 moles

Now we can rearrange the Ideal Gas Law equation to solve for temperature (T):

T = PV / (nR)

Substituting the given values:

T = (111.42 kPa * 57.09 L) / (1.485 moles * 8.314 J/(mol·K))

Calculating this expression, we find:

T ≈ 902.56 K

To convert the temperature to Celsius, we subtract 273.15 from the Kelvin temperature:

Temperature in °C = 902.56 K - 273.15

≈ 629.41 °C

Therefore, the temperature of the hydrogen gas produced is approximately 629.41 °C.