Element X reacts with hydrogen gas at 200°C to form compound Y. When Y is heated to a higher temperature, it decomposes to the element X and hydrogen gas in the ratio of 559 mL of H2 (measured at standard temperature and pressure) for 1.00 g of X reacted. X also combines with chlorine to form a compound Z, which contains 63.89 percent by mass of chlorine. Deduce the identity of X. The symbol of element X is

X is calcium with the symbol Ca

Explanation:

From the first statement:

X reacted with H2 to produce Z i. e

X + H2 - > Y

Y is heated to form X and H2 i. e

Y - > X + H2

Let us obtain moles of H2 produced. This is illustrated below:

Volume of H2 produced = 559 mL = 0.559 L.

I mole of H2 occupy 22.4L at stp

Therefore, b mol of H2 will occupy 0.559 L at stp i. e

b mol of H2 = 0.559/22.4

b mol of H2 = 0.025 mole

Next 0.025 mole of H2 to gram ...

Molar Mass of H2 = 2x1 = 2g/mol

Mole of H2 = 0.025 mole

Mass = number of mole x molar Mass

Mass of H2 = 0.025 x 2

Mass of H2 = 0.05g

From the question given, we were told that 1g of X reacted. This means that 1g of X reacted with 0.05g of H2. Now let us determine the mass of X that will react with 1 mol (i. e 2g) of H2. This is illustrated below:

From the reaction,

It was discovered that 1g of X reacted with 0.05g of H2.

Therefore, P g of X will react with 2g of H2 i. e

P g of X = 2/0.05 = 40g/mol

The molar mass of X is 40g/mol.

Now let us consider the second statement to see if we'll obtained the same result as 40g/mol of X

From the second statement:

X also combines with chlorine to form a compound Z, which contains 63.89 percent by mass of chlorine i. e

X + Cl2 - > Z

Molar Mass of Z (X + 2Cl) = X + (35.5 x 2) = X + 71.

Z contains 63.89% by mass of Cl2.

We can obtain the molar mass of X as follow:

Percentage by mass of Cl2 in the compound Z is given by:

Mass of Cl2/Molar Mass x100

63.89/100 = 71 / (X + 71)

Cross multiply to express in linear form

63.89 (X + 71) = 100 x 71

Clear the bracket

63.89X + 4536.19 = 7100

Collect like terms

63.89X = 7100 - 4536.19

63.89X = 2563.81

Divide both side by 63.89

X = 2563.81/63.89

X = 40g/mol

Now we can see that in both experiments, the molar mass of X is 40g/mol.

Comparing the value of X i. e 40g/mol with that from the periodic table, X is calcium with the symbol Ca