A 0.160-g sample of unknown metal (X) reacts with hydrochloric acid to produce 66.5 mL? Help please
Sure! To solve this problem, we need to determine the molar mass of the unknown metal (X) using the given information.
Let's start by using the given information to calculate the number of moles of the unknown metal (X) that reacted with hydrochloric acid.
Step 1: Convert the given volume of hydrochloric acid to moles.
The volume of hydrochloric acid is given as 66.5 mL. To convert this volume to moles, we need to use the molar volume of an ideal gas at standard temperature and pressure (STP), which is 22.4 L/mol.
66.5 mL = 66.5 mL * (1 L / 1000 mL) = 0.0665 L.
Thus, the volume of hydrochloric acid is 0.0665 L.
Now we can calculate the number of moles of hydrochloric acid using the molar volume at STP:
n(HCl) = V(HCl) / V_m (HCl)
where n(HCl) is the number of moles of HCl, V(HCl) is the volume of HCl, and V_m (HCl) is the molar volume of HCl at STP.
Using the given information, we can now calculate the number of moles of HCl:
n(HCl) = 0.0665 L / 22.4 L/mol = 0.002965 mol.
Step 2: Calculate the number of moles of the unknown metal (X).
We can use the balanced equation between the unknown metal and hydrochloric acid to determine the stoichiometry of the reaction. Let's assume the balanced equation is:
2HCl + X → XCl2 + H2
From the balanced equation, we can see that 2 moles of HCl react with 1 mole of X. Since we have calculated the number of moles of HCl in Step 1, we can determine the number of moles of X.
n(X) = n(HCl) / 2 = 0.002965 mol / 2 = 0.001483 mol.
Step 3: Calculate the molar mass of the unknown metal (X).
The molar mass of a substance is the mass per mole. Given that the mass of the unknown metal (X) is 0.160 g and the number of moles is 0.001483 mol, we can calculate the molar mass using the equation:
Molar mass (X) = Mass (X) / moles (X)
Molar mass (X) = 0.160 g / 0.001483 mol = 107.96 g/mol.
Therefore, the molar mass of the unknown metal (X) is approximately 107.96 g/mol.
To determine the identity of the unknown metal (X), we can use the concept of stoichiometry. Stoichiometry is a mathematical relationship between the quantities of reactants and products in a chemical reaction.
To find the identity of the metal X, we need to calculate its molar mass. We can do this by performing the following steps:
1. Determine the number of moles of hydrochloric acid used: The given volume of hydrochloric acid is 66.5 mL. However, we need to convert this volume to moles. To do this, we need to know the concentration of the hydrochloric acid (in units of moles per liter).
2. Construct the balanced chemical equation: Write the balanced equation for the reaction between the metal X and hydrochloric acid. This will give us the stoichiometric ratio between the metal and the acid. The equation should be something like:
X + HCl → XCl + H₂ (where XCl represents the chloride compound of the metal X)
3. Use the stoichiometry of the balanced equation to find the number of moles of metal X: Convert the moles of hydrochloric acid obtained in step 1 to moles of metal X using the stoichiometric ratio from the balanced equation.
4. Calculate the molar mass of the metal X: Divide the mass of the metal X (given as 0.160 g) by the number of moles of metal X obtained in step 3.
By following these steps, you will be able to determine the molar mass and identity of the unknown metal (X) based on its reaction with hydrochloric acid.