Question

Question: One way to purify gaseousH₂is to pass it under high pressure through the holes of a metal’s crystals structure. Palladium, which adopts a cubic closest packed structure, absorbsH₂ 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 H₂measured at STP, can be packed into the spaces of of palladium metal?

Short answer

Answer

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

Step-by-step solution

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.

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

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

calculation for volume of gaseous hydrogen

Calculate the volume at STP by using ideal gas equation.

Since at STP

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

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

Ideal gas equation,

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

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