Question

A 0.136 g sample of an unknown metal (X) reacted with excess hydrochloric acid according to the following balanced chemical reaction:

2X(s) + 6 HCl(aq) → 2XCl₃(aq) + 3 H₂g) The volume of hydrogen gas collected over water was 90.5 mL at 20°C and a barometric pressure of 756 mmHg. Determine the atomic mass of the unknown metal. Use the Periodic Table of
A 0.136 g sample of an unknown metal (X) reacted with excess hydrochloric acid according to the following balanced chemical reaction:

2X(s) + 6 HCl(aq) → 2XCl₃(aq) + 3 H₂(g)

The volume of hydrogen gas collected over water was 90.5 mL at 20°C and a barometric pressure of 756 mmHg. Determine the atomic mass of the unknown metal. Use the Periodic Table of elements to identify the metal.

Answer 1

To determine the atomic mass of the unknown metal (X), use the ideal gas law to calculate the number of moles of hydrogen gas produced. Then, calculate the molar mass of the unknown metal X using the mass of the sample and the number of moles. The atomic mass of the unknown metal X is approximately 0.041 g/mol.

Step-by-step explanation:

To determine the atomic mass of the unknown metal (X), we need to use the ideal gas law to calculate the number of moles of hydrogen gas produced:

PV = nRT

Where:

• P = pressure = 756 mmHg
• V = volume = 90.5 mL = 0.0905 L
• n = number of moles of H2 (since 3 mol H2 are produced for every 2 mol X)
• R = ideal gas constant = 0.0821 L·atm/(mol·K)
• T = temperature = 20°C = 293 K

Solving for n:

n = (PV) / (RT)

n = (756 mmHg * 0.0905 L) / (0.0821 L·atm/(mol·K) * 293 K)

= 3.318 mol H2

Now, we can calculate the molar mass of the unknown metal X using the mass of the sample and the number of moles:

molar mass of X = mass of X / moles of X

molar mass of X = 0.136 g / 3.318 mol

= 0.041 g/mol

Therefore, the atomic mass of the unknown metal X is approximately 0.041 g/mol.