Question

Given the first order reaction is completed 90% in 30 mins at 298K . Calculate the rate constant ?​

Answer 1

Answer:

(ᴀ)

ʀᴀᴛᴇ ᴄᴏɴꜱᴛᴀɴᴛ

ꜰᴏʀᴍᴜʟᴀ ꜰᴏʀ ʀᴀᴛᴇ ᴄᴏɴꜱᴛᴀɴᴛ

ᴋ=ᴛ2.303ʟᴏɢ10(ᴀᴏ−xᴀᴏ)

ɢɪᴠᴇɴ ᴛ=25 ꜱᴇᴄ

ʟᴇᴛ, ᴀᴏ=100 (ꜱɪɴᴄᴇ ɪɴɪᴛɪᴀʟ ᴠᴀʟᴜᴇ ɴᴏᴛ ɢɪᴠᴇɴ)

x=90 (90% ʀᴇᴀᴄᴛɪᴏɴ ᴄᴏᴍᴩʟᴇᴛᴇᴅ)

ᴀᴏ−x=100−90=10

ꜱᴜʙꜱᴛɪᴛᴜᴛɪɴɢ ᴛʜᴇ ᴠᴀʟᴜᴇꜱ

ᴋ=252.303ʟᴏɢ10(10100)

ᴋ=252.303×1{ʟᴏɢ1010=1}

ᴋ=0.09212 ꜱᴇᴄ−1

(ʙ)

ʜᴀʟꜰ ʟɪꜰᴇ ᴩᴇʀɪᴏᴅ

ꜰᴏʀᴍᴜʟᴀ ꜰᴏʀ ᴛ1/2=ᴋ0.693

ꜱᴜʙꜱᴛɪᴛᴜᴛɪɴɢ ᴠᴀʟᴜᴇ ᴏꜰ ᴋ ꜰʀᴏᴍ ᴀʙᴏᴠᴇ

ᴛ1/2=0.092120.693

ᴛ1/2=7.5228 ꜱᴇᴄ