a student heats 2.005 g of a copper bromide hydrate of unknown molecular formula, completely driving off the water of hydration, and notices that the weight drops to 0.998g. Upon reduction with excess aluminum metal, the copper ions are reduced to 0.442 g of Cu (s). determine the formula of this unknown copper bromide hydrate

2.005 = mass CuxBry + H2O

0.998 = mass CuxBry
----------
1.007 = mass water

CuxBry + Al ==> Cu + ...not balanced.
0.998g.........0.442
moles Cu = 0.442/atomic mass Cu = about 0.007 but you need to be more exact.
So mols CuxBry must be 0.007

n = grams/molar mass and
molar mass = grams/n = 0.998/0.007 = about 143 or so for molar mass CuxBry.
143 = mass Cu + mass Br
-63.5 = mass Cu
------------
79.8 = approximate mass Br which is one Br so the formula must be CuBr.
Find moles CuBr (0.998/molar mass) = ?
mole H2O = 1.007/18 = ??
Now find the ratio H2O to 1 mole CuBr. The easy way to do this is to divide the smaller number by itself (which gives you 1.000) and divide the other number by the same small number. Round to whole number. That should give you x in CuBr.xH2O.

Why did the math book become so thirsty? Because it had too many problems to solve! Anyway, let's tackle this question together.

First, let's determine the weight of water that's being driven off. The initial weight of the copper bromide hydrate was 2.005 g, and after heating, it dropped to 0.998 g. So, the weight loss is 2.005 g - 0.998 g = 1.007 g.

The molar mass of water is approximately 18 g/mol, so to find the moles of water lost, we divide the weight loss by the molar mass:
1.007 g / 18 g/mol ≈ 0.056 moles of water.

Now, let's find the moles of Cu that's been reduced. The weight of Cu produced is 0.442 g, and the molar mass of Cu is approximately 63.5 g/mol. So, the moles of Cu is:
0.442 g / 63.5 g/mol ≈ 0.007 moles of Cu.

To find the moles of bromide (Br) present in the compound, we need to convert the moles of Cu to moles of Br. Every mole of copper bromide formen contains one mole of copper and two moles of bromide. So, we can say that:
1 mole of Cu = 2 moles of Br.

Since we have 0.007 moles of Cu, we can calculate the moles of Br as:
0.007 moles of Cu × (2 moles of Br / 1 mole of Cu) = 0.014 moles of Br.

Now, let's find the moles of copper bromide (CuBrx) that was present in the compound. We know that the moles of water lost (0.056 moles) must be equal to the moles of copper bromide (CuBrx) present. Therefore, x must be equal to:
0.056 moles.

Given that we have 0.014 moles of Br, we divide it by the total moles of CuBrx to find the empirical formula:
0.014 moles of Br / 0.056 moles of CuBrx = 0.25.

Since we want a whole number ratio, we multiply all by 4:
0.014 moles of Br / 0.056 moles of CuBrx × 4 = 0.056 moles of Br / 0.224 moles of CuBrx.

This means the empirical formula is CuBr4. Therefore, the molecular formula of this unknown copper bromide hydrate is CuBr4 · 4H2O.

Hope that helps! Let me know if you have any more questions.

To determine the formula of the copper bromide hydrate, we need to calculate the number of moles of copper, bromide, and water in the hydrate.

1. Calculate the number of moles of copper:
The molar mass of copper is 63.55 g/mol. Divide the mass of copper (0.442 g) by the molar mass to get the moles of copper.
Moles of copper = 0.442 g / 63.55 g/mol ≈ 0.00696 mol

2. Calculate the number of moles of water:
Water has a molar mass of 18.015 g/mol. Subtract the mass of copper bromide after heating (0.998 g) from the initial mass (2.005 g) to find the mass of water lost.
Mass of water lost = 2.005 g - 0.998 g = 1.007 g
Divide the mass of water lost by the molar mass of water to find the moles of water.
Moles of water = 1.007 g / 18.015 g/mol ≈ 0.0559 mol

3. Calculate the number of moles of bromide:
To find the moles of bromide, we need to determine the moles of bromide in the copper bromide hydrate compound. The moles of bromide are equal to the moles of copper since copper bromide has a 1:1 ratio of copper to bromide.
Moles of bromide ≈ 0.00696 mol

4. Determine the empirical formula:
Divide the moles of each element by the smallest number of moles.
Copper: 0.00696 mol ÷ 0.00696 mol ≈ 1
Bromide: 0.00696 mol ÷ 0.00696 mol ≈ 1
Water: 0.0559 mol ÷ 0.00696 mol ≈ 8

The empirical formula of the copper bromide hydrate is CuBr · 8H2O.

To determine the formula of the unknown copper bromide hydrate, we need to analyze the given information. Let's break down the steps:

1. Calculate the mass of water lost:
Mass of water lost = Initial mass - Final mass
Mass of water lost = 2.005 g - 0.998 g
Mass of water lost = 1.007 g

2. Convert the mass of water lost into moles:
To convert grams to moles, we need to know the molar mass of water.

The molar mass of water (H2O) is approximately 18.015 g/mol.
Moles of water lost = Mass of water lost / Molar mass of water
Moles of water lost = 1.007 g / 18.015 g/mol
Moles of water lost = 0.056 mol

3. Calculate the moles of Cu formed:
Moles of Cu formed = Mass of Cu / Molar mass of Cu
Moles of Cu formed = 0.442 g / Atomic mass of Cu

To find the atomic mass of Cu, we can refer to the periodic table or use an online resource. The atomic mass of Cu is approximately 63.546 g/mol.

Moles of Cu formed = 0.442 g / 63.546 g/mol
Moles of Cu formed = 0.00695 mol

4. Determine the mole ratio between Cu and water:
The mole ratio between Cu and water can be obtained by dividing the moles of Cu formed by the moles of water lost:

Mole ratio = Moles of Cu formed / Moles of water lost
Mole ratio = 0.00695 mol / 0.056 mol
Mole ratio ≈ 0.124

5. Deduce the formula of the copper bromide hydrate:
From the mole ratio, we can deduce the formula of the copper bromide hydrate.

The formula of the hydrate is: CuBr2·xH2O

We need to determine the value of x. The mole ratio tells us that there is approximately 0.124 moles of water for every 1 mole of copper.

To find the value of x, we need to divide the moles of water by the moles of copper:

x = Moles of water lost / Moles of Cu formed
x = 0.056 mol / 0.00695 mol
x ≈ 8

Therefore, the formula of the unknown copper bromide hydrate is CuBr2·8H2O.