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Hi mastorak136 and welcome.
No, an i7 processor is not compatible with your model.
Your Vaio VGN-NW21SF has an Intel Core 2 Duo processor P7450 which fits into a Socket 478. The PGA478 socket is incompatible with the newer i3/i5/i7-series processors - you would need a new motherboard (is one exists).
Hi mastorak136 and welcome.
No, an i7 processor is not compatible with your model.
Your Vaio VGN-NW21SF has an Intel Core 2 Duo processor P7450 which fits into a Socket 478. The PGA478 socket is incompatible with the newer i3/i5/i7-series processors - you would need a new motherboard (is one exists).