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Answer:
ᴀᴘᴘʟʏ ᴛʜᴇ ғᴏʀᴍᴜʟᴀ ᴘᴠ=ɴʀᴛ
ᴠᴏʟᴜᴍᴇ ᴏғ ɢᴀs ᴀ = ᴠᴀ = ɴᴀʀᴛᴀ/ᴘᴀ
ᴠᴏʟᴜᴍᴇ ᴏғ ᴅɪʜʏᴅʀᴏɢᴇɴ = ᴠ = ɴʀᴛ/ᴘ
sɪɴᴄᴇ ᴠᴀ = ᴠ
ɴᴀʀᴛᴀ/ᴘᴀ = ɴʀᴛ/ᴘ
ᴘ=ᴘᴀ sᴏ ɪᴛ ᴡɪʟʟ ᴄᴀɴᴄᴇʟ ᴏᴜᴛ.
ʀ ᴡɪʟʟ ᴀʟsᴏ ʙᴇ ᴄᴀɴᴄᴇʟʟᴇᴅ ғʀᴏᴍ ʙᴏᴛʜ sɪᴅᴇ.
ɴᴀ = ɴᴛ/ᴛᴀ
ᴘᴜᴛᴛɪɴɢ ᴛʜᴇ ᴠᴀʟᴜᴇs ɪɴ ғᴏʀᴍᴜʟᴀ :
ɴ= 0.184/2
ᴛ= 17+273 = 290ᴋ
ᴛᴀ = 95 + 273 =368
ɴᴀ= 0.184/2 * 290/368 = 0.0725
ɴᴀ= ɢɪᴠᴇɴ ᴍᴀss ᴏғ ɢᴀs / ᴍᴏʟᴀʀ ᴍᴀss ᴏғ ɢᴀs
0.0725 = 2.9 /ᴍᴏʟᴀʀ ᴍᴀss ᴏғ ɢᴀs
ᴍᴏʟᴀʀ ᴍᴀss ᴏғ ɢᴀs = 2.9/0.0725 = 40ɢ
Explanation:
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Let mass of unknown gas is = m
M(g) = 5.40 gm
T(g) = 27℃ = (273 + 27)K = 300K
V(g) = V(H) = V
P(g) = P(H) = P
M(H) = 0.14 gm
T(H) = 17℃ = (17+273)K = 290K
- Here, 'g' refers to the unknown gas
- and, 'H' refers to the Hydrogen Gas.
Now, For the unknown gas:
P(g)×V(g) = n×R×T(g)
=> PV = M(g)/m × RT(g) ................(i)
For Hydrogen gas:
P(H)×V(H) = n×R×T(H)
=> PV = M(H)/1 × RT(H) ..................(ii)
Since LHS of (i) and (ii) are equal, there hence, their RHS must also be equal.
That is,
M(g)/m ×RT(g) = M(H) ×RT(H)
=> M(g)/m × T(g) = M(H) × T(H)
=> 5.4/m × 300 = 0.14 × 290
=> (5.4×300)/m = (290×0.14)
=> 1620/m = 40.6
=> m = 1620/40.6
= 39.901 gm
≈ 40 gm
Hence, molecular mass of the unknown gas is 40gm.