Question

a closed vesswl having capacity200ml is filled with hydrogen gas STP. calculate:
number of moles of hydrogen gas filled in the vessel
pressure of hydrogen gas in the vessel ai 273 degree c
root mean square velocity of hydrogen gas at STP
the value of Cp and Cv for hydrogen gas

Answer 1

Answer on Question #60517, Physics /

a closed vessel having capacity 200ml is filled with hydrogen gas STP.

calculate:

number of moles of hydrogen gas filled in the vessel

pressure of hydrogen gas in the vessel at 273 degree C

root mean square velocity of hydrogen gas at STP

the value of Cp and Cv for hydrogen gas

Find: $v - ?p - ?u - ?Cp - ?Cv - ?$

Given:

$V = 200 \times 10^{-6} \mathrm{~m}^{3}$

$M = 2 \times 10^{-3} \mathrm{~kg} / \mathrm{m}^{3}$

$T_0 = 273 \mathrm{~K}$

$P_0 = 10^5 \mathrm{~Pa}$

$R = 8,31 \mathrm{~J} / \mathrm{mol}$

$T = 273 + 273 \mathrm{~K} = 546 \mathrm{~K}$

$N_A = 6,02 \times 10^{23} \mathrm{~mol}^{-1}$

$k = 1,38 \times 10^{-23} \mathrm{~J} / \mathrm{K}$

$i = 5$

Solution:

Equation of state for ideal gas:

$$p_0 V = \frac{m}{M} R T_0$$

Number of moles:

$$v = \frac{m}{M}$$

where M – molar mass

Of (1) and (2) $\Rightarrow v = \frac{p_0 V}{R T_0}$

Of (3) $\Rightarrow v = 8,8 \times 10^{-3} \mathrm{~mol}$

Pressure of hydrogen gas:

$$p = n k T$$

Concentration:

$$n = \frac{N}{V}$$

Number of molecules:

$N = v N_A$

Of (6) $\Rightarrow N = 53 \times 10^{20}$

Of (5) $\Rightarrow$ n = 0,26 × 10²⁶ $\frac{1}{\mathrm{m}^3}$ (8)

(7) and (8) in (4): $p = 200 \times 10^3$ Pa

Root mean square velocity:

$$u = \sqrt{\frac{3RT_0}{M}} \quad (9),$$

where $T_0 = 273$ K (gas at STP)

Of (9) $\Rightarrow$ $u = 1840 \, \text{m/s}$

Molar heat of the gas at constant volume:

$$C_v = \frac{i}{2} R \quad (10),$$

where $i$ – number of degrees of freedom

Of (10) $\Rightarrow$ $C_v = 20,78 \, \text{J/K}$

Molar heat of gas at constant pressure:

$$C_p = \frac{i + 2}{2} R \quad (11)$$

Of (11) $\Rightarrow$ $C_p = 29,08 \, \text{J/K}$

**Answer:**

number of moles: $u = 8,8 \times 10^{-3}$ mol

pressure of hydrogen gas in the vessel at 273 degree C: $p = 200 \times 10^3$ Pa

root mean square velocity of hydrogen gas at STP: $u = 1840 \, \text{m/s}$

the value of $C_p$ and $C_v$ for hydrogen gas: $C_v = 20,78 \, \text{J/K}$, $C_p = 29,08 \, \text{J/K}$

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