If a #21*g# mass of calcium hydride is reacted with excess water, (i) what mass of calcium hydroxide will result; and (ii) what volume of dihydrogen will be evolved at #"STP"#?

Question

Jeremiah Adams · Accepted Answer

B. 37 g of #"Ca(OH)"_2# are produced; C. 23 L of #"H"_2# gas are formed at STP.

A. Equilibrium formula The equation that is balanced is #"CaH"_2("s") + "2H"_2"O"("l") rarr "Ca(OH)"_2("aq") + "2H"_2("g")# B. Mass of #"Ca(OH)"_2# #"Moles of CaH"_2 = 21color(red)(cancel(color(black)("g CaH"_2))) × ("1 mol CaH"_2)/(42.09 color(red)(cancel(color(black)("g CaH"_2)))) ="0.499 mol CaH"_2#. #"Moles of Ca(OH)"_2 = 0.499 color(red)(cancel(color(black)("mol CaH"_2))) × ("1 mol Ca(OH)"_2)/(1 color(red)(cancel(color(black)("mol CaH"_2)))) = "0.499 mol Ca(OH)"_2# #"Mass of Ca(OH)"_2 = 0.499 color(red)(cancel(color(black)("mol Ca(OH)"_2))) × ("74.09 g Ca(OH)"_2)/(1 color(red)(cancel(color(black)("mol Ca(OH)"_2)))) = "37 g Ca(OH)"_2# (2 significant figures) C. Volume of #"H"_2# #"Moles of H"_2 = 0.499 color(red)(cancel(color(black)("mol CaH"_2))) × ("2 mol H"_2)/(1 color(red)(cancel(color(black)("mol CaH"_2)))) = "0.998 mol H"_2# STP has been defined by the IUPAC as 1 bar of pressure and 0 °C since 1982. In these circumstances, an ideal gas has a volume of 22.71 L per mol. ∴ #"Volume of H"_2 = 0.998 color(red)(cancel(color(black)("mol H"_2))) × ("22.71 L H"_2)/(1 color(red)(cancel(color(black)("mol H"_2)))) = "23 L H"_2# (2 significant figures) The volume of #"H"_2# at STP is 23 L.

Luna Chen · Answer

undefined (i) The balanced chemical equation for the reaction between calcium hydride ($ \text{CaH}_2 $) and water ($ \text{H}_2\text{O} $) is:

$$ \text{CaH}_2 + 2\text{H}_2\text{O} \rightarrow \text{Ca}(\text{OH})_2 + 2\text{H}_2 $$

From the equation, it can be seen that one mole of calcium hydride reacts with two moles of water to produce one mole of calcium hydroxide.

Given that the molar mass of calcium hydride ($ \text{CaH}_2 $) is approximately 42.09 g/mol and the molar mass of calcium hydroxide ($ \text{Ca}(\text{OH})_2 $) is approximately 74.10 g/mol, you can calculate the mass of calcium hydroxide produced using the given mass of calcium hydride.

$$ \text{Mass of calcium hydroxide} = \frac{21 \text{ g} \times 74.10 \text{ g/mol}}{42.09 \text{ g/mol}} $$

(ii) According to the balanced chemical equation, one mole of calcium hydride produces two moles of dihydrogen gas ($ \text{H}_2 $).

Since the reaction takes place at STP (Standard Temperature and Pressure), one mole of any ideal gas occupies 22.4 liters.

Thus, the volume of dihydrogen gas produced at STP can be calculated using the ideal gas law:

$$ \text{Volume of dihydrogen gas} = \frac{2 \times 22.4 \text{ L}}{42.09 \text{ g/mol}} \times 21 \text{ g} $$

Remember that STP refers to a temperature of 0°C (273 K) and a pressure of 1 atm (101.3 kPa).