Q 12.145 P - Chemistry: Molecular Nature Of Matter And Change

Question

Question: One way to purify gaseous H₂ is to pass it under high pressure through the holes of a metal’s crystals structure. Palladium, which adopts a cubic closest packed structure, absorbs H₂ than any other element and is one of the metals currently used for this purpose. Although the metal-hydrogen interaction is unclear, it is estimated that the density of absorbed H₂approaches that of liquid hydrogen (70.8g/L). what volume (in L) of gaseous H₂ measured at STP, can be packed into the spaces of of palladium metal? 

 

Step-by-Step Solution

Answer

Answer

 

795.26 L volume of gaseous H₂ can be packed into the spaces of $1d{m}^3$of palladium metal.

Step 1: Definition

 

Density is word used to describe how much space an object or substance takes up in relation to amount of matter in that object or substance. The mass-to-volume ratio is known as the density. A three-dimensional figure's volume is the amount of space it takes up, expressed in cubic units.

Step 2: calculation of mass of hydrogen

 

In the question given value of density is$70.8g/L$ and volume of spaces of palladium metal is $1d{m}^3$ (1L). So, mass of hydrogen gas can be calculated as 

$$\begin{gathered} \text{density}=\frac{\text{mass}}{\text{volume}} \\ \text{mass}=\text{density}\times \text{volume} \\ =70.8 g/L\times 1L \\ =70.8 g \end{gathered}$$ 

 

Step 3: calculation for volume of gaseous hydrogen

 

Calculate the volume at STP by using ideal gas equation.

Since at STP 

 $$\begin{gathered} T=273K \\ P=1 atm \\ R=0.082 L.atm/mol.K \end{gathered}$$

 $$\begin{gathered} \text{Moles of hydrogen}=\frac{\text{mass}}{2} \\ =\frac{70.8}{2} \\ =35.4\text{moles} \end{gathered}$$

Ideal gas equation,

          $$\begin{gathered} PV=nRT \\ V=\frac{nRT}{P} \\ =\frac{35.4mol\times 0.082 L.atm/mol.K\times 273K}{1 atm} \\ = 795.3L \end{gathered}$$

Therefore, the voids of $1d{m}^3$ of palladium metal can hold 795.26L volume of gaseous H₂.