Question

A 0.125−g sample of aluminum-zinc alloy is placed in the same apparatus used in lab this quarter. The hydrogen gas generated by the reaction with hydrochloric acid displaces 152.8 mL of water into a beaker (at 21 ∘

C). The vapor pressure of water at this temperature is 18.7 mmHg. The barometric pressure is 759 mmHg. a. b. What is the percentage of aluminum in the sample?

Answer 1

The percentage of aluminum in the sample is approximately 10.1%.

Step-by-step explanation:

The displacement of water in the beaker results from the reaction of aluminum with hydrochloric acid:

`\[2\,Al + 6\,HCl \rightarrow 2\,AlCl_3 + 3\,H_2\]`

The volume of hydrogen gas collected is related to the moles of aluminum through the ideal gas law (PV = nRT), where (P) is the pressure, (V) is the volume, (n) is the number of moles, (R) is the gas constant, and (T) is the temperature. We need to adjust the volume of hydrogen gas collected to standard temperature and pressure (STP) conditions (0 °C

and 1 atm). Using the combined gas law,
`\(P_1V_1/T_1 = P_2V_2/T_2\)`, we can calculate the volume of hydrogen gas at STP, which is equivalent to the moles of aluminum.

Now, we convert moles of aluminum to grams and then determine the percentage of aluminum in the alloy by dividing the mass of aluminum by the total mass of the alloy and multiplying by 100.

It's crucial to account for the vapor pressure of water in the displacement, subtracting it from the atmospheric pressure to find the true pressure exerted by the hydrogen gas.

In this case, the percentage of aluminum is found to be approximately 10.1%, indicating the composition of aluminum in the alloy.

Answer 2

To determine the percentage of aluminum in the sample, we can use stoichiometry. By calculating the number of moles of hydrogen gas produced and the number of moles of aluminum, we can find the percentage of aluminum in the sample, which is approximately 35.0%.

Step-by-step explanation:

To determine the percentage of aluminum in the sample, we need to use stoichiometry. Let's start by finding the number of moles of hydrogen gas produced. We can use the ideal gas law, PV = nRT, where P is the pressure (in atm), V is the volume (in L), n is the number of moles, R is the gas constant (0.0821 L·atm/mol·K), and T is the temperature (in Kelvin). From the given data, we have the volume of water displaced (152.8 mL = 0.1528 L), the vapor pressure of water (18.7 mmHg = 0.0247 atm), the barometric pressure (759 mmHg = 1 atm), and the temperature (21°C = 294 K).

First, we need to calculate the pressure of hydrogen gas:

Total pressure = barometric pressure + vapor pressure of water = 1 atm + 0.0247 atm = 1.0247 atm

Next, we can rearrange the ideal gas law to solve for the number of moles of hydrogen gas:

n = (PV) / (RT)

n = (1.0247 atm * 0.1528 L) / (0.0821 L·atm/mol·K * 294 K)

n = 0.00579 mol

Since the stoichiometry of the reaction is 3 moles of hydrogen gas per mole of aluminum, we can calculate the number of moles of aluminum:

n(Al) = (1/3) * n(H2)

n(Al) = (1/3) * 0.00579 mol

n(Al) = 0.00193 mol

Finally, we can calculate the percentage of aluminum in the sample:

Percentage of aluminum = (mass of aluminum / total mass of sample) * 100%

Since we have the mass of the alloy sample (0.125 g) and the molar mass of aluminum (26.98 g/mol), we can use the equation:

Percentage of aluminum = (0.00193 mol * 26.98 g/mol / 0.125 g) * 100%

Percentage of aluminum ≈ 35.0%